St Andrews William & Mary Joint Degree Programme

Does anyone know if admissions there is any advantage or disadvantage if I apply for the joint programme through St. Andrews instead of through William and Mary? And if I apply through St. Andrews, is it possible for St. Andrews to accept me to their university but reject me for the joint programme?

I know people who did their first year of their WAMSTA program in St Andrews and then decided they wanted to stay in St Andrews so consequently re-applied to just St Andrews.

They didn’t get in to St Andrews so have to stay on the WAMSTA programme.