Realistically, they probably just sing an approximation that's close to JI while unconsciously allowing the pitch to drift a little bit so that comma pumps aren't a problem.

That seems more plausible than that people naturally sing in an artificial tuning based on repeated multiplication of the twelvth root of two, even if that's the musical context that people are most exposed to these days. Those whole-number ratios are just too good to resist, even if a singer isn't fully aware of what they're doing.