When you print, a "screen,projection" stylesheet won't be used at all - it will be ignored. You don't have to override its values from print CSS, you're starting again with an unstyled page.
The only screen-based CSS browser I know of that doesn't work with screen-media is Netscape 4 - ns4 doesn't read any styles if the <link> element has a media attribute, but that's useful in itself.
There are extra gotchas as well - some handheld devices read "screen" media CSS, even though that's clearly in violation of the specs. But some manufacturers think that if they don't do that, pages viewed from their PDAs might not be styled at all - which is true, and that would be probably be better for users than a screen-styled page. But there you go - vendors are only concerned with their own, narrow interests.
"Why bother with accessibility? ... Because deep down you know that the web is attractive to people who aren't exactly like you." - Joe Clark