I think some light behind the screen is ok, ie a dim glow, not so much that it finds its way onto the front. This may even be preferable to a batcave, for two reasons:
1. Your eyes have a dynamic iris (which you can't switch off

). If it is really dark then obviously your irises will open to allow more light in, and you will "get used to the dark". This will make you more aware of the dim glow that is a projected black screen.
2. Lots of black velvet provides a reference black that will contrast with the almost-black of the screen.
Clearly you don't want any unprojected light to hit the screen, via reflections and so on, as it will affect your C/R, there is no doubting that. But the "no light whatsoever, ever!" is not necessarily nirvana either.
To test this out I've created two images to simulate an almost-black screen, one in a batcave and one with a light wall behind. The grey looks blacker in the latter case (ideally the pics should be viewed in total darkness, so that your eyes get used to the dark, but if you look close up and block out light with your hands it gives an idea of the effect I'm talking about). This is an extreme case, as such a light wall would probably spill light onto the screen, but the principal is the same.
PS you may need to adjust your contrast/brightness to see the grey rectangle