PayPal might be a private company but it still needs authorizations from governments and central banks, since it is linked to your bank account, i really think in a situation where cryptocurrency becomes a trend and a lot of people start using them, PayPal will just create their own coin just like Facebook is doing right now and the same as probably all the other companies, but in a situation where bitcoin becomes accepted i don't see why they won't some other banks and payment systems are already doing it like Neteller.