What game are we playing here?
There are two classes of argument posted so far:
1. The characters, having failed a save, believe the illusion. The players are bound by the characters, and must not attempt to reverse their fate.
2. The characters, while not immediately perceiving an "illusion" per se, can still deduce that something is amiss, and will go to all ends to test their reality, eventually pulling a thread that unravels the entire narrative...
Both assume that the rules act as an intermediary between the players and the DM, to determine who "wins" the encounter. I think this is entirely missing the point of D&D. The game, at least when you're slaying the vampire and looking for his magical weapon, is about looting tombs. Under the circumstances, I would expect characters to tear apart a crypt to find a weapon. Are these characters "realistic?" No. They're psychotic. But that's what you get when you play D&D: a bunch of guys who always do the right thing, and the right thing always happens to be killing a bunch of folks and taking their stuff.
The DM's role is not to "beat" the party. If the party, having burned the "body," discover the treasure isn't there, they may never learn anything about that body's nature. But they're sure as hell going to trash the place anyway looking for treasure.
The DM seemed to be worried that in doing so they would discover that the body was an illusion, and that the vampire was still alive and, presumably, nearby. Tough luck for the vampire, not for the game, or for the DM. Who cares if it's metagaming? Who cares what's a mind-affecting illusion, a phantasm, or a glamour (this GM is obviously using extreme house rules anyway, so those arguments are moot)? You don't need to justify the character's acting in a strange fashion in the pursuit of treasure, even if a normal person would NEVER EVER EVER act that way. Because they're not normal people: they're heroes. It's not meta-game, it's the game.