As your link puts nicely: "John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together."
Cool! That’s an interesting idea. I could see particular attributes of DNA being corrected, but How would a molecular basis for inheritance be disproven? After all, we see the molecule on microscopy, we modify it, etc. A dis-proof would have to remain consistent with all of that. What would that look like?
So it could be disproven, but will it? No. It definitely exists. But could it? Yep, that's how we know it exists in a scientific context. It's a bit counterintuitive, but it's the language of science. You see it in how physicists talk about discoveries - how many sigma they are. That's basically saying how likely it is the null hypothesis (sort of the falsification of the discovery) is true - and there's a point where it's so low (5 sigma traditionally) that it is considered "discovered." But that discovery is qualified with the chance that it's falsifiable.
I don't know if that was a clear explanation - if not let me know so I can try clarifying. It was something that took me a while to wrap my head around - that it's only demonstrable if falsifiable, but it's a core part of a lot of scientific theory today
Will a future experiment disprove it though? Of course not. But could one? Sure. There's an important distinction.
Also, we could end up redefining what we mean by a mountain, or come to some scientific consensus that somehow redefines mount Everest as not a mountain or something. I know that's not in the spirit of the question you posted (Pluto may be declared to not be a planet, but nothing actually changed and it doesn't know we put it in a different bucket). The height could be redefined, etc. All that is super nitpicky and of course, I'm being a bit unreasonable in this response, there will not be any experiment that disproves its existence. But there still could. In the binary of is there any possibility however minuscule or not, the coin lands on the side of there is a possibility.
The important point is falsifiability works as a tool here that actually helps continuously support the mountain's existence. If it was impossible to falsify and you could not conduct experiments where you would be able to evaluate whether or not the mountain is actually there, you'd have no way of being actually sure. One experiment is just looking at it. You could not see anything and falsify it, but because it's a testable hypothesis, you have run an experiment providing more evidence for its existence. It's why non-falsifiable statements are looked down on science. If it wasn't possible for a future experiment to disprove the existence of the mountain, many or all scientists would say it's either a meaningless question or a question of faith instead.
And Einstein definitely falsified Newton with the famous experiment with the eclipse and with more correctly showing Mercury's orbit, both of which contradicted fundamentally with Newton. Newton is an extraordinary breakthrough, and still useful as a model, but our understanding is no longer Newtonian. And, finding a way to enrich our understanding of physics even further means finding ways to falsify parts of einstein and quantum mechanics to provide the foundation for an even deeper understanding.