Advisor transferring to better school
The other school is hiring your adviser because they think they'll be a good researcher and faculty member. This means that at some level they trust your adviser's judgement.

It's not impossible, but it'd be highly unlikely that they would refuse to admit you against your adviser's request. The more likely situation, if they're concerned about your ability, is that they would ask to have you repeat some courses or milestones like an oral exam or portfolio review.

When they hire your adviser they're essentially saying that they're impressed with their research program. It'd be a little self-defeating to hire that person but say that they can't bring substantial portions (the students) of that effort.