Karl H said:
...."Fuses and breakers just protect the wire."...
The boss is somewhat correct. And so are you.
As IW and Jon said, you're right in that the overloads protect the conductors from, well, overloads. The also do a marginallly poor job at protecting the motor from overloads (an opinion). Repeated overloading of a motor with proper NEC sized overloads will lead to motor catastrophic failure. The conductors will likely be fine.
As IW said, the CB protects the wire from Short Circuit and Ground fault. The CB also protects the structure and the people.
It the motor develops a short or a ground fault, there is no motor to save - it's dead. The conductors however may still be good. The CB should be sized to open before the wire is damaged. This is what your boss is talking about. Most of the stuff I work are not laid out to the NEC. Rather there is a coordination scheme. The generator damage curve, Gen CB protective relays, feeder CB, ovld, wire damage curves are carefully laid out to insure the protective relays trip with minimum equipment damage. Notice I didn't say no equipment damage. Same goal as the NEC, just some different equipment to protect.
Now, about protecting the structure and people: If the motor dies attempting to turn into a molten pile of slag, or if the conductors die in a backhoe attack and turn into an arcwelder, the job of the CB is to put the fire out - save the structure, save the people inside of the structure.
Philosophy time (where's my brother the philosopher when I need him?)
The mission of the protective devices is always the same:
1. Protect the people
2. Protect the structure
3. Protect the conductors
4. Maybe Protect the device (last on the list)
5. Keep the system making money as long as possible