I think Just intonation, or an approximation to that, is what people are instinctively using, unless they are consciously tuning themselves to a piano.
It sounds much more "in tune" to the ear, because of the nice ratios.
It really wouldn't surprise me that raw recordings of many singers are in fact more just than equal temperament.
This makes sense, but it would imply that they have "instinctively solved" the fundamental problems with modulation and harmony that just intonation creates. This seems unlikely.
You might find the book "How Equal Temperament Ruined Harmony" interesting, which presents a reasonably strong case that pre-1900s western music treated enharmonics as distinct pitches ("enharmonic" in the old sense seems to have referred to the distinction). Singers knew about major and minor semitones, and they knew where to place commas. Though, no one seemed to go as far as doing full just intonation due to various kinds of obvious and non-obvious impracticalities.
All in all, I think it's safe to say that string players and singers prefer slightly flatter thirds in harmonies than 12-EDO -- which is what the above amounts to -- and deal with commas accordingly.
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.
It sounds much more "in tune" to the ear, because of the nice ratios.
It really wouldn't surprise me that raw recordings of many singers are in fact more just than equal temperament.