@bdeeley is correct. And IME most RBC employees are unfamiliar and poorly informed concerning the foreign operations of the parent bank. They just can't see them on their branch network, so assume they are not the same. RBC US and RBC Financial Caribbean are separate incorporated banks, different from the domestic operatoins in Canada, for legal and regulatory reasons. They do not share branch operations, so yes, they are not the "same" bank, but they do work with clients of other RBC banks on a preferred basis.

When I pull money out of an RBC ATM in Sint Maarten, I am charged a witthdrawal fee, unlike here at home. But ulitmately, as @bdeeley says, they are all subsidiares of the parent bank. I was able to park in the parking lot at the branch in Philipsburg, reserved for RBC customers, by simply showing them my domestic RBC Client Card, so there is some recognition.