I was playing a game of Commander with my friends a while ago and I had a Seal of Doom in play alongside a Starfield of Nyx and enough enchantments to make all my enchantments creatures. My opponent throws a creature removal spell at my Seal of Doom. In response I use Seal of Doom's activated ability and sacrifice it in order to destroy a creature. My opponent then responds by playing Snakeform on it.
My friend says that i can't activate its ability since it's no longer Seal of Doom and the ability reads "Sacrifice Seal of Doom: Destroy target creature". But isn't the cost payed once the ability goes on the stack and therefore isn't Seal of Doom already in the graveyard before his instant spell resolves? Or am I wrong and can you counter an activated ability this way?