Did they specify they'd take responsibility for cross-contamination? I'd be shocked if a bakery made that assertion without being able to back it up, what with all the liability issues. I'd try calling them back and find out if they have a history of working around allergies and that they understand the severity of the issue; it's likely that they know they're doing...or a few probing questions should make it clear that they don't.
I can't blame you for being reticent, though - nut allergies are a particularly scary thing, and can sneak up on you, as other posters here will attest. We have quite a number of kids in our school that have severe contact allergies to various foods, which I'm glad to say our school is handling gracefully.