I just rebuilt a P125 engine and the rear hub is rubbing on the backing plate.
You know the raised ridge all the way around the circumference of the backing plate that fits into a groove in the hub to create a barrier to dust and moisture? That is where it is rubbing. I don't know if this was happening before the rebuild.

Could new O-rings be thick enough to cause backing plate to be too far out?
What else could cause this to happen?

This is for a customers scooter. If it was mine, I would maybe ride it around to see if took care of itself.

The only time I have had this happen was when I didn't tighten the screws that hold the backing plate into place enough. Double check those three screws. I had one come out due to not tightening it enough which caused a loud grinding sound.

The backing plate could be bent. I know, I know--it doesn't come into contact with anything, so how could that be? It just happens sometimes.

Take a look at the backing plate. If it's been happening for a while, then a portion of that lip will be nicely polished. If it's something that happened due to the rebuild, then that same contact patch won't be as shiny.