The original thread was about finding a "single bank" and in that regard, it is not a problem to open a bank nearly anywhere, including in Europe (assuming legal residence there). Brokers, that might be a different matter, if you wish to trade European stocks from a European account. Taxes can be the added hassle of having to file in the U.S. regardless of where you live, but we were originally discussing getting a bank account, which is straightforward.
You're right, they can't find a bank because they don't have a visa that allows them to work. It is common for people to say they "live" somewhere while doing visa runs, leaving and re-entering the country, in order to remain.
It's unfortunate that this statement [1] is so prominently placed in this thread. That's social media for you I guess.
[1] "I have friends who cannot find a single bank in their country that will work with them because of the reporting requirements of working with US citizens"
Yeah Americans in particular are famous around the world for choosing to live in places they have not tried to legally reside in, and so much of these anecdotes are likely coming from stories like that.
Even in the U.S. it can be very hard if not impossible to open a bank account with an American bank if you are not legally living there, so the shoe fits on both feet.