This is a tricky situation. however, I would suggest you go with your gut instinct! Do you think you have heartache ahead with this one?
Could you tell your tenants that they are responsible for her moving in therefor if anything happens they have to cover rent etc (not even sure you can do this so im open to correction).
Inform all your tenants that the PRTB is necessary, however this new girl they have brought in is refusing to sign. It might be no harm to make everyone aware (but do all this in a really nice way)