The rules specifically say that melee attacks are "clamped in place" (1st sentence under "Vehicles, Gun Emplacements, and Monstrous Creatures" BRB 180)
In other words, melee grenades are not thrown. Every model can attack with it.
Also, I realize this is very indirect so I risk weakening my point, but I still think this is relevant: look at the paragraph long explanations under every single grenade type. Every shooting description specifies that a single model replaces their attack with the grenade, and none of the melee descriptions make any such statement.