Absolutely agree ("the player must maintain possession to make the catch, even in the ez") but for how long? Sorry, but if the player (airborne or not) establishes possession (of a live ball in flight) and first touches the ground in-bounds, while maintaining that possession IT IS A CATCH.
If those things ALL happen in the EZ, it's a TD and the lights shut off. If those same things happen in the field, the lights stay on and all sorts of things can effect what happens next.
If there is ANY question about possession being consistent (maintained) all bets are off, and the pass is incomplete, but when a player stumbles, falls AFTER completing the required sequence in the EZ, or beyond the sideline causing possession to be interrupted, the interruption happened to a DEAD ball.