I tried to copy the existing stylesheet created for the Twenty Twelve parent theme into the child theme’s file
You can do that as long as you change the header for the style.css to what it must be for a Child Theme, and then WordPress reads your sheet first and checks it against the one in the Parent to be sure nothing gets missed on the way to the screen.
I wonder if it really is picky about the space after the colon? I may have to play around and test that theory
Could be, and I do know it just rejected one of mine (saying the Parent was missing) when I had TwentyTwelve where twentytwelve should have appeared as the name for its Template.
@ibit: I named my Child Theme nny2012child and activated it, and then cloned (download) it and made nny2012trial (and then uploaded that one) as the place I can make changes and test things without losing what I already have if something might go horribly wrong. But if you might decide to do something like that, remember that the two headers are different when copying one into the other! I made that mess for myself twice today.