I think Travolta has been flying his jets for more than 120 days.
If the FAA site shows he has a PPL then he has a PPL, and same for certain other cases which have recently come up
Completely legal too (for Travolta) - a PPL can fly a 747 RHS if he has a TR. An ATPL is needed only to be a Captain (LHS). Obviously not for paying passenger carriage.