Jim,
Your description of the rating of circuit breakers is true. But, nevertheless you may NOT put a 60A rated breaker on a 50A rated circuit, if that is what the circuit is rated (wire sizes enter in to the situation, among other things). Fault current/short circuit study evaluations are also a factor when sizing breakers, as well as whether or not ground or neutral might be involved, or whether we are talking a line breaker or load breaker. An electrical inspector that spots something like this
will fail the inspection, industrially or commercially. Equipment in question would have to be shut down immediately.
Inspectors can and do make mistakes that help or hurt owner/operators, and I can testify on this from over 40 years experience/exposure, but the code seems pretty clear here. By the way, the code with regard to cirbuit breaker rating is hotly contested (nothing new) whenever the NEC makes a revision. Whether or not something is a code violation is often argued, even by IEEE and/or NEC contributors, but I think this is an 'easy' one.
We need to be very careful when recommending electrical protection advice. The easiest way to stay out of trouble is to stay at or below current or voltage ratings.
Now I'm done on this one.