As davidbeach indicated, it's a lot more complicated than can be determined with what you are able to tell us, but to answer your question generally, ground faults can come in all sizes and flavors, as does ground fault protection equipment. If the protection equipment you have does not specifically look for the type of ground fault you had (or can have), it will not protect for it.
For example, take your motor overload relay and circuit breaker for instance. In some scenarios, a ground fault can take a high resistance/impedance pathway, meaning the current flowing to ground is not terribly high. If that's the case, and the total current flow to ground is at or below the thermal overload threshold of your OL relay, there is no reason for the relay to trip. And if it's too low for the OL relay to trip, it is definitely too low for the either the thermal or magnetic trips on the circuit breaker as well.
In another scenario, even if you had one lead of the motor branch circuit going to ground and you have a corner grounded delta system to start off with, and the phase that was mis-wired was the one that referenced to ground anyway, that might look only like a single phased system to the motor starter, not a ground fault. If your motor is relatively unloaded (i.e. under 58% load), a basic NEMA style motor starter would think that is just hunky-dory.
Your scenario makes it sound as though your company needs to hire a PE to do a system coordination study to ensure that any potential problem like this will be seen and reacted to by your protection equipment. That's what coordination studies are all about. If I were you and your bosses, I would not fool around and try to be cheap about this, there appear to be some serious deficiencies in your system as a whole, i.e. a fire just looking for an excuse to happen.