My interpretation was not that they can force Billups to return to the planet and perform as king, but that their laws would name him as their king and he is not willing to be negligent in his duties if he is named king because of his personal character.
In the long term, this may mean eventually he will return and become king when it is required of him, but he was trying to delay that and follow his own interests for as long as possible, since the planet currently has a functional and effective ruler: his mother.
This is why he agreed to go through the process of becoming king when he believed his mother had died, again reluctantly, but still choosing to fulfill his duties to respect his family and the needs of the people he would be ruling over, as there is no exploration of alternative heirs or loopholes or workarounds in their legal system.