Innate sense of harmony? Hmm. The ancient Greeks, we are told, thought that the major third was dissonant (do I mean discordant?). And Ptolemy knew the JI major third was 5/4, but the Pythagoreans couldn't get 5/4 out of 2 and 3/2, so they never bothered with it, lol!
I'm told Suk's serenade for strings requires certain passages to be played with JI so that different parts of the orchestra harmonise with each other in different ways. I should imagine a singer can do it with the right accompaniment, although it might be harder for them than for a violinist who always has to fudge between their JI open strings and whatever ET piece they are playing.
When I was 12 I had a friend who had perfect pitch. He wasn't musical - they just had a piano in the house, so I've always assumed it was just an eidetic memory thing.
Pavarotti apparently had it and insisted on using it, but as a result there are recordings where he is so much sharper than his accompaniment that I can't listen to them.