I am not sure why her citizenship is such an issue as she most likely would have went to the Olys either way as a single skater or a pairs skater. She is certainly better than Buchanan.
It wouldn't have been enough to be better than Buchanan. Paige would have needed to be much better than Buchanan to qualify for the Olympics as a singles skater. Buchanan is only able to go because Israel qualified in three disciplines. If Paige had not skated pairs, then Israel might not have qualified in three disciplines. Paige would have had to do so in ladies singles. She was only 27th at Junior Worlds & didn't qualify for the free skate there so I think it's clear Paige made the stronger choice for her own future and that of the Israeli team.