Yes, it is possible. You can be a permanent resident your entire life and not qualify to apply for citizenship. Usually, that invovles a criminal record, but there are other disqualifying factors.
Andrew Sullivan is a Permanent Resident, but disqualified from citizenship because he has HIV, to pick one example.
Though, in this case, I think that any irregularities can be fairly overlooked. He’s been here since 1987 (as a child, I assume, given his present rank and career). He’s seemingly been vetted and all of that.