If you're DMing for the right reasons, this will rarely happen.Take priority over his/her responsibility? Yeah, quite probably.
Take equal priority? Hmmm... Now friction is occurring, and things are a lot more grey (and is probably the majority of situations, AFAIC).
When push comes to shove (i.e. beyond compromise - which, we all agree, is the first solution), whose right to have a good time wins out? The DM? The players? The DM and the majority of players?