Heh, I can't add too much to the discussion because I don't actually remember what the issue was, but I have definitely had one rejected. Might have missed a layer or something.
If you violate the design rules in a way that they can still try to manufacture, they almost always will. If you use a 5mil trace on a 6mil minimum, they won't care, they'll make it anyway. Remember - the minimum is just set by the point at which the yield starts to fall. It's actually often a perfectly valid endeavor to violate this minimum on purpose and just accept the low yield. I've done it before, when I was having ten boards made and only needed one anyway. There are plenty of posts online from people who have done this intentionally to try to make use of some part, typically a BGA, that was technically impossible within the supplied specifications.