OT - Not true, at least in my dad's case. He had a PPF account with SBI but no savings account. He used to easily transfer money to and from his IDBI Bank savings account to his PPF account in SBI.
Two years ago, PNB were trying to make us open an account with them to claim inheritance money from my grandfather's account. They started by citing a rule that they don't transfer money to another bank's account if amount is above 50k. I showed them documents downloaded from PNB's website itself which showed same was only true in case amount was more than 5L and made them transfer the amount to my SBI bank account.