Agreed. But the argument put forward was that without the cultural heritage you cannot be considered bilingual. That is what I am disagreeing with.
I have over 50 years very close experience with language professionals: translators, academics, diplomats, foreign correspondents... I think I have met only three who claimed to be bilingual, and one of those (a linguistics lecturer) was deluding himself because he had an accent so thick none us could understand him. Our other lecturers included UN interpreters. They did not claim to be bilingual. Their awe was reserved for a colleague who could interpret simultaneously between two languages while doing a crossword in a third language while in the booth. These people included several who were boastful of their language ability, but they had other ways of expressing it. One I was tickled by was a diplomat who kept repeating, "I speak Arabic, AND I read Arabic and write Arabic." Others would stress that they were PROFESSIONAL translators.
My language colleagues seemed to reserve bilingualism to describe having two native languages from birth. Myself, I relax the criteria a bit, but I still think the number of bilingual people I have met who were not born in that environment amounts to only between one and two dozen. The normal phrase I use to describe even the highest level of language ability acquired after birth is "totally fluent", but as I say I have softened my standards a little.
Just "fluent" is not all that high for me - say 1-dan amateur in go. This may be to do with the generation game. When I started learning languages the emphasis was on grammar ("construe this Latin, boy!") and speaking was almost an optional extra. Even at university courses would emphasise literature, arts, religion - actually speaking was for the proles.
That changed over several decades so that now speaking is emphasised heavily and cultural aspects are relatively neglected. Whether that's good or bad is obviously a matter of opinion, but I do notice that one feature of people who are proud of being "fluent" is that they are rather poor at reading what is written. We see that all the time on this forum. They just seem to "flow" over a text and get merely an impression of what they read, and answer that instead of what was actually written. I also think the lack of deeper understanding of foreign cultures is potentially harmful, although it is masked somewhat by the whole world now becoming more and more uniform, and of course more people do travel and broaden the mind nowadays.
I also remember Margaret Thatcher complaining bitterly, in the early days of dealing with Gorbachev, that there was nobody in Britain's universities who could explain the Soviet economy properly to her. There were plenty of people who spoke Russian fluently and others who knew the economics jargon, but none who had the necessary cultural background to convey what it meant to be a Soviet person having to survive on a daily basis in the USSR.
But hey (to use an Americanism), I can get around the USA without a dictionary or an interpreter. Wow! (another Americanism - does this fluency mean I'm bilingual?) Seriously? (another Americanism - make that multilingual, and I might as well claim to be 9-dan go pro while I'm at it since I could solve the tsumego tami posted today instantly).