As a grounded conductor, still have to question the setup, as the OP says the #4's land on the MCC ground bus. Of course the OPer could be mistaken by thinking it is a grounding conductor because that is also where the GEC terminates... but instead lands on a neutral bus (should be mounted with stand-off insulators and have a main bonding jumper). Could also be an MCC designed for 3? 3-wire (non-compliant).
You are correct, it is the neutral, not the ground that has been brought to the MCC. The customers GEC lands on the same bus within the MCC.. and the MCC does not have a neutral bus.
For right now my main concern is the size of the GEC. I assumed that table 250.66 is used but from Denis' post (he says use #6) I must be mistaken...