Interesting question. I'm certainly not a 'natural' musician but over the years I've developed the ability to instinctively work out the chord sequence (or the chords that fit)for any song I want to sing. Once I've found a suitable key, it usually just falls into place, not least because there are only a few that will fit, so it's a matter of elimination. (I'm not talking jazz here with its seemingly unlimited 9ths, 13ths, diminisheds etc) It's very rare for there to be a traditonal or traditional-type song that has a 'weird' chord slotted in. If I have do have a problem, I'm lucky in that I can simply ask my middle son, who has perfect pitch, what he's hearing that I'm not.

But I would stress that it's years of practice and experience. I suppose playing in a folk-band, i.e. for dance, has helped - when the accordian player suddenly went into a tune I've never heard before, I would go into automatic pilot and follow the basic melody using just the three or four chords that the key calls for. In fact, it was rare to be told the name of the tunes we'd be about to play - it was usally 'DGAM'(keys of D, G,then into Am)or 'G all the way.'