Tested it in psxjin202 using a Director's Cut version and it worked on about a 20th attempt. No idea what is the cause of this, but Barry just stops on a 2nd screen. Was recording a movie, so maybe there is a way to look into it. Dropping the pjm in just in case:
http://dl.dropbox.com/u/17623935/re1skip.zip
EDIT: the skip happens as early as you get in the item select screen. No matter what you do next, Barry has already stopped near the clock by that moment and no cutscene will be played. I'll fiddle with it more.
EDIT2: Ok, there is a 1-frame window in which you have to press the start button. From what i've tested, it appears that all what's needed is this one buttonpress. Coordinates & other buttons do not matter. Also if you reenter the room without triggering the zombie FMV, the cutscene with blood gets played.
So, i suppose the main reason which allows for a cutscene skip is that Barry is too far away from a blood pool. And when you exit the room, the game just puts him there, and upon reentering the cutscene is triggered. Wonder what causes him to stop in the first place.