As said in LD 2x07 Where Pleasant Fountains Lie, Billups is from Hysperia and there is still the technicality that can force him on the throne.

This kind of condition makes me wonder what Hysperia’s political status with the Federation is. What stops Billups from e.g claiming asylum with the Federation, especially considering the Hysperians are not a powerful force?

I have three theories:

• Hysperia is a Federation colony, so they are able to apply their throne law on Billups and Billups is unable to claim asylum with a political entity he was already born into.
• Hysperia is not a Federation member, but has a scare resource (like dilithium) that makes Starfleet want to maintain good relations with Hysperia.
• Alternatively, it could be some sort of weird prime directive thing.