Don't think that undermines my claim at all - they understand the words because they're familiar within the slavic language group in general (even though they might be derivations and used or spelled differently). Its like saying Italian/Spanish are the same because speakers might understand words between them. With the translation argument - you also of course have to ignore the fact that Serbia writes in cyrillic and Croatia in latin alphabet.
Basically, the point is about what defines a language as a distinct one.
Grammar is pretty much the same with one standard preferring one form or the other (eg. infinitive vs "da" + present). Vocabulary is over 90% identical, though I am sure top 500 words in both spoken dialects have a larger discrepancy. Alphabets are different, but they are almost bijectively mapped (only differ orthographically in digraphs like NJ/Nj/nj where Cyrillic has only Њ/њ), and you may have missed it, but Serbian population actually uses Latin script for >80% of all Serbian writing.
The article mentions a push to differentiate languages further, probably most evident in Croatia in early 90s.
But three students in Bosnia speaking identical language (grammar/vocabulary thougj the script might differ) of 3 different nationalities would officially claim they speak three different languages. If you don't see the absurdity in that, that's up to you.
Also, doesn't your claim that BCS speakers are attuned to different dialect groups and understand their terms even further undermine the claim that there's an actual need for translation? By and large, speakers of English aren't (although thanks to Hollywood everybody knows some American), but an Aussie in NYC or a Brit in Melbourne is not going to have any real issues communicating.