Ya know... I work at a shop that's licensed by a major university and we run into this problem constantly.
Yes, your shop is liable if you print something copyrighted because you are "responsible" for what you print. It doesn't matter whether it's a logo, slogan, photo, or money (here in the US) - if the customer does not own the rights to what they are printing, you cannot print it.
Also, if you are licensed to print something that's copyrighted - say a logo - and use it in your artwork, etc, it can only be used in YOUR artwork; I can't use it in MY artwork and then have you print it.
It's important to determine what is copyrighted as well: it's obscene just how much stuff is actually protected by copyright. Of course we all know that if I take a photo and put it on Facebook, technically I own the rights to it, but it's gone WAY beyond that - to the point that I'm being intentionally vague about it because I can't say with certainty that I know what all is copyrighted
Edit: didn't realize I was digging up an old-ish thread - my bad!