The PAG is irrelevant. The OP is looking to get the points and credit for the night. The T&Cs are clear that the hotel does not have to give the PAG on the second night, but that has nothing to do with closing out the first folio and starting a new folio. The second folio just won't have a PAG.

FWIW I often get credit for the second PAG even after letting the front desk know I understand I should not.