In my view, "boarding early" means being ready fairly close to the gate when the preceding zone is called for boarding – not sneaking into a group boarding for an earlier zone. Then when his zone is called, he will be, if he is prepared, one of the first in his zone to board. That should usually assure overhead space for a carryon.

In this case, if he was truly in the last zone to board, he may well have been in E+, already populated by some with status who legitimately boarded with an early group. Still, it's very likely there would still have been storage space if he had been one of the first of those in his boarding zone to get on.

Having been burned once, my guess is he will be much less likely to have a problem next time, especially if you give him some guidance.