Crikey, I was told by the band leader of a Bluegrass band that he didn't want me to play an EUB because it spoiled the aesthetic of the band - which was otherwise old-fashioned acoustic instruments - which I get, but it must be a pretty obsessive punter who gets arsey about Jazzes versus Precisions.
Having said that, there's a few candidate bands that are 100% associated with Precisions, and I could imagine punters being obsessive enough to point out the issue, so if I was in a tribute to any of those I'd simply take the easier route and play a Precision, especially as it would probably sound more authentic.
Of course, we don't know which band it is so we can't tell.........