Look at it this way, though. Balazar has a power that says:
When you defeat a monster and would banish it, you may add it to your hand instead.
If the monster has a power that prevents it from being banished, it doesn't still go into Balazar's hand, because you would not banish it. It can only replace the "banish" with "add it to your hand" if the banish was going to happen in the first place. In the case of Rez, if something prevents burying, you don't get to activate her power because you would not bury it. You can not replace "bury" with "discard"/"recharge" unless you could have buried it in the first place.
What makes this read as a trigger is you would, but "when". In order for "When you would do something" to apply, it has to be legal to do the something and in this case doing the something is not legal, so this is not a time when you would do it.