Honestly, report every player who thinks they own a role/champion in question.
I usually don't ban my teammates' own picks but if they're last or second to last and i know this is a highly contested pick, it's very likely they're not going to get it BUT we're going to have to play against it.
Now, Riot also knows to whom the roles have been assigned to and there's chat logs in champ select to prove that someone hijacked someone's role. Don't think that these people are getting away with it and Riot does punish such behavior more severely than toxicity. I usually (after reporting them) also submit a support ticket if i come across such a player because there are no specific categories there and i want to make sure this player is in RIot's crosshairs.
Also, don't back down and give them the role.
Pick your champion you intended to and go where you've been assigned to go. If the game is already going to be a loss because of this behavior, don't allow them to get away with it and don't leave the queue and taking the LP penalty yourself. If you do this, they are absolutely getting off without a punishment as Riot then has no game as evidence to pin it on their ass.