if you want to use the lfg tool then yes you will need to satisfy the trinity.
when I used my 5 locks I had to go to each dungeon myself! but I didn't mind as it was my first foray into cata/panda content.
subsequent teams all satisfied the trinity though, its too inconvenient not being able to use lfg. (but so what if players want to take an unorthodox premade into an instance!) totally understand the restrictions for pugs though.