I've had one experience with this, and that was during my first Thousand Maws. Everyone except maybe the healer had never done the dungeon before. I heard battle music and the sounds of combat, and got a 15 second warning that the boss room was about to lock. Note, there is zero indication that you wont be locked out of the boss fight until the party wipes or wins. So I agonized for a couple seconds before saying "screw it, I'll watch the cinematic in the inn later" and skipped it. That way I could get in and try keeping whoever was fighting alive. This is how I learned that the healer is the one who'd jumped the gun. Since I was playing pugilist (was only in the early 20's), I didn't have much of a tool kit yet. But I used what I did have to try pealing aggro off the healer. The 2nd DPS joined in next, an archer I think. Which meant we were throwing attack after attack to try pulling the boss off our healer who was unable to stop moving long enough to throw out any heals, and desperately trying to kite to stay alive in the process. By the time our tank was in the fight, the healer had been downed for too damn long and I was about to go down as well. Needless to say, we wiped. And our healer blamed the wipe on the 3 of us for "wasting time watching useless cutscenes. Nobody cares about the story, it doesn't matter at all." Until I mentioned it, the other two players didn't even know you could rewatch cinematic in the inn. They thought that if you miss a cut scene, it's gone forever.

Moral of the story? Not only is it rude to jump the gun while the party is watching cinematic, it can in fact cause party wipes.