I almost agree on the danger. I understand the concern if they are putting rock on the back side of that wall, I am just not sure the code actually backs him up. It sounds like he is trying to stretch the protection of cables (300.4) to boxes and misapplying 110.27(B)
A 2.5" deep box would not be compliant either then.
I doubt it would survive an appeal.
Ask him, "if the guy sistered op a short piece of 2x4 to the stud and nailed the box to that, would it be OK"?
That would give you 1.5" from the nearest edge of the framing member. It is not that I think that is what I would make them do but it might give you better insight into his thinking.
He may just not like plastic boxes. I have seen crusty old guys like that.