I think a general rule when deciding whether or not to play for free under any circumstance should be that you instigate the proceedings yourself.
Many times, I've struck up a tune in a bar, quiet cafe, or some other nice space but it's more often been for my own benefit and enjoyment rather than anyone eles's. I've also chosen to join sessions or take part in charity events with others where I know I won't be getting paid.

It's a different story, if a bar or cafe approached me and asked if I would perform for nothing. I would be reluctant to do such a thing. Not just for my own sake but I'd be concerned that I might be doing another musician out of a job.

The same applies to approaches by other organisations like those discussed here, in my opinion. If a musician or singer feels they need extra exposure, surely they would want to seek out opportunities for themselves and make whatever arrangements they wish. If then they felt that it was worth their while in the long run to work for nothing on a particular occasion, fair enough, but that's their choice.