Yes, but he's not making that determination based on what a law says--rather, only based upon his own determination. It's irreverent that such a power to deny comes from a statute. Prohibited by law = law says no. Suitability = Chief says no.
I see what you're getting at and while I think it's a plausible interpretation, when we talk about "prohibited by law or regulation from possessing a firearm", we're talking PP territory--as in "operation of law"--not pursuant to law.
Let me try putting this another way: Say my LTC gets revoked for suitability, but I had an FID card that (up until last week) was not revokable. What then?
Whatever the case, this potential confusion should be fodder for arguments of you NH folk.
What if you never took the Mass firearms safety class? You cannot get an FID or LTC without it and therefor prohibited from possessing firearms?