It took me a bit to figure out why fíor was used with either the copula or bí because it is initially taught to us as an adjective. I found out fíor is either a noun that means "truth" or an adjective that means "true". The above sentence is thus more along the meaning of "that is truth" even if this is awkward in English. Correct?
Is there any preference to use the copula or bí among native speakers?
Well, I don't really get what "it is true that" means (non-native English speaker, sorry), but I'm pretty sure is fíor é sin means "that is true", because é sin corresponds to "that". So I think "it's true that" is more of a calque than a good translation, but I can't tell for sure.
It's a full sentence in Irish, but ‘it is true that’ is not a full sentence in English. You could say ‘it is true, that’, but that's not really standard English.