In this context Ben Folds "on top of the beat" is referring to Scott pushing the beat a little, i.e. getting a fraction ahead or rushing a bit, but it's only something you'd notice if you listen very closely. Scott is probably nervous and sometimes when he's singing a rhythmically faster passage it's not quite synchronized with the rest (around 2:00). The whole group gets a bit out of sync around 3:03. If he'd been a little more relaxed the performance would have been even better, but this is still an excellent performance and Ben's criticism is intended constructively (he has to say something).
Exactly where a singer places the notes in relation to the rhythm section is a matter of stylistic taste. In a pop song you would generally want to be "on the beat" but not ahead of it ("on top of the beat"). Jazz singers tend to go in the opposite direction. They will sing very slightly behind the beat or "laid back". Frank Sinatra was a master of this and learned it early in his career when he was singing with the Tommy Dorsey Band. As arranger Sy Coleman said:
I was trying to get Frank to fall in with the lazy sort of two-beat feeling - the Lunceford beat. All kid singers tend to push too hard, and so one day I suggested ' Lay back on it, Frank'. And you know what? He literally laid back with his body. Then I explained to him what I really meant, to lay back on the beat, not to push but to let the beat sort of carry him along... must say he caught on right away.
DrummerCafe has a discussion of this with examples
A Jazz trio with the bass playing on top of the beat (which works in this context)
Drummer Eric Harland has a video demonstrating this in a Jazz context.