The Vasconic Substrate Hypothesis suggests that Basque was a major language in Europe from prehistory or at least the neolithic, and that it influenced most modern European languages. That's rather a stretch, modern western European languages are mostly a mix between Indo-European variants and Latin, to a larger or smaller degree. Claiming another pre-indo-european layer under all that, I mean, sure, maybe, but it is diluted to an extent that makes it rather irrelevant.
The evidence for that is very weak, it depends how literally you interpret it. I think it is arrogant to suggest that those ancient languages were basque, rather modern basque has some distant roots in those pre-into-european languages. In my opinion, the more correct way of expressing it would be that this proto-basque was part of a large family of related languages spoken in Europe during the neolithic. There is no proper evidence that proto-basque was widespread, it's just that it is the only preserved remnant from that linguistic era at large.
This is mostly a theoretical exercise, extrapolating back patterns observed in Latin loanwords changed after being absorbed and differences between modern dialects.
Brief parenthesis: There are still significant differences in the language within a couple hundred km, to the point where it can be very hard to understand each other. An effort was made during the 60s to define a Standard Basque (Euskara Batua: https://en.wikipedia.org/wiki/Standard_Basque) for education, bureaucracy and law. It is comparable to the unification of Mandarin Chinese at a smaller scale.
Back to the topic of older basque. You have to consider that there's a clear record of the basque living under roman rule, and the region has been under larger powers (but also relatively isolated and autonomous) for its entire history. The intermixing with romance languages started all the way back with original Latin, and the discovery discussed in the article also shows heavy influence from pre-roman iberian languages in the use of their alphabet, even if the languages probably had different roots (iberian is indo-european, basque not).
Nevertheless, the language in this discovery is not really considered basque but more of an ancestor. There is a large gap in the written record, very little has been found between early Roman times and the first writings in modern Basque well into the Middle Ages, at which point heavier intermixing with the rest of Europe started during the 1500s with the pioneering of large-scale whaling and a thriving ship-building economy. It's not really clear when modern basque started, and it has been heavily influenced by other languages pretty much since the neolithic.
(Kind of embarrassing to ask here since I'm a spaniard and I should know more, but since you're already discussing it...)
But I have friends from inner Gipuzkoa with a very strong accent, and it's pretty hard to understand people from Zuberoa (one of the French provinces) and particularly certain towns and small cities (not always rural) from inner Bizkaia (where Bilbo is).
Not sure how much they stick to Batua in school, but at least it seems like their family and environment has a bigger influence. Of course they understand Batua but tend to stick to their regional dialect when speaking.
But no, it is definitely not limited to the older generation.
On diffs on writting in "Standard" and speaking, Andalusia can be hardcore mode too, specially Cadiz. A Uni student can have a vastly different register on writting for terms at class compared to the day to day speaking.
I understand that there is not enough extant Iberian[1] for it to be classified. Did you mean Celtiberian[2]
[1] https://en.wikipedia.org/wiki/Iberian_language [2] https://en.wikipedia.org/wiki/Celtiberian_language
This effort has been relatively successful. A significant majority of students do all their studies, including university, fully in basque. There are many families that exclusively speak basque at home. And traditional basque public holidays and sports are prominent, popular, and frequent throughout the year.
There is a serious concern however, that Basque is becoming entrenched into a language only for education, bureaucracy and family life. It is much less popular in the streets and between friends, especially in the capitals of the provinces. This is partially affected by the significant reduction in funding for basque TV, films and dubbing, especially when it comes to cartoons for young children, as well as sketch comedy, which were so influential to my generation (funnily enough, basque dubbed anime was quite big!).
Nevertheless, the fertility-rate in the Basque country has actually been one of the lowest in Europe for the last few years. The conversation around it is more about the economy than culture. It is already seriously affecting primary schools, which are starting to compete a lot more and some closing down. There are bigger problems in the public conscience lately (COVID, Ukraine, recession...), and it will take at least another generation for the consequences of the low fertility rate to be felt, but there is an awareness of looming demographic trouble.
Another one of those classic HN quotes!
There are a few factors.
Generally the Spanish basque provinces have a significantly larger population, larger economy and more autonomy than the French provinces. In France Basque is not an official language in the region and is only available with private schooling. France is also very Paris-centric and very little support is given to the fringes. In Spain we keep the vast majority of our taxes, have our own local parliament and president, as well as fully independent social security, healthcare, police and education, almost all in basque, public and private.
As a result, the vast majority of support for Basque has been focused on the Spanish regions, which might have increased the separation. There is indeed a Standard Basque defined during the 60s for education, media and governance. Not sure if she is referring to this, it did consider all seven major dialects, including the French ones, but it is quite biased to the dialect from the central province (Gipuzkoa) and is significantly different to dialects at the edges of the region, to the point where mutual comprehension is a legitimate challenge.
The French dialects also have, well, a strong French accent, including different vowels, I also struggle to understand them. Whereas the Spanish dialects have almost the exact same phonemes as Spanish. It would probably sound like Spanish to a non-speaker, even if the grammatical differences are vast.
It is also possible that she is referring to the fact that many people in the Spanish provinces just don't speak Basque very well. This is actually because of a positive achievement: most students study in basque now. The thing is that often their parents don't speak it, they tend to become friends with others with Spanish speaking families, and they end up just using Basque for school. And in school they learn to understand the language and write it well, but struggle to speak it, often with a heavy dose of Spanish elements and sentence patterns.
None of this is all that new though, unless by "recent years" she means the last 30, which is not unreasonable.
Ziberuan dialect = hard mode.
Labort dialect = easy-medium mode to understand Batua.
Also, if a Batua speaker it's used to speak the Western subdialect (Biscaian) and unadvertedly introduce "jargon" into Batua, it would be difficult because that dialect has lots of Latin/Castillians borrowings.
Spanish has similar issues too. Pick up a Chilean/Argentinian "chav" and partner it with a Murcian teen guy. If they mainly speak in their subdialects, either guys will have a hard time, even if both speak Spanish.
OFC if they keep a conversation on "semi-standard" Spanish they'll understand the 99%, 100% if both are speaking about academic terms or just a random serious article/news in a newspaper/web site.
Still, the RAE dictionary in Spain is huge, it covers ALL the manerism/idioms/jargon of Spanish all over the world, so any speaker from Mexico to the Patagonia or Iberia can easily query the online RAE dictionary for local terms such as molar, rentar, pasada, chévere, chido, tío (not in familiar terms), bacán and so on.
Let me know if you are curious about anything, I am happy to answer.
I am obviously biased as a native speaker, but I am surprised it is considered the hardest language to learn. Yes sentences have an unusual order, and most pronouns and determinants are embedded as postfixes of other words, especially verbs. However, phonetically it is almost indistinguishable from Spanish at this point. The alphabet is latin and each letter directly corresponds to a single sound (except for silent h). Spelling is "as it sounds", very consistent and much simpler than other languages I have learned. The vocabulary includes large quantities of romance (from latin, mostly Spanish) loan words that will sound familiar to most Europeans. And the sentence structure and vocabulary are often (incorrectly) streered towards Spanish/French patterns in casual speech.