At the end of the movie where they are all singing "We go together", they are all walking toward the camera, and the pink ladies are on one side and the greasers on the other. A second or 2 before they switch angles, the 2 groups switch sides...
I think the author of this Slip-up used the term "greaser" as a mix-up with this movie and "The Outsiders". Characters in the movie/book were a lot like the T-Birds and they called themselves greasers.
Actually, the greasers are just a general term for the pink ladies and the T-Birds in the actual script of the play. So the person probably just got them confused, they weren't technically wrong.