BYU, BYU-I and BYU-Hawaii are not separate campuses of the same institution. They are 3 separate institutions that are part of the Church Educational System. That is exactly why people get irritated when "BYU-P" is used as it insinuates that it is simply one of 3 main campuses.

As an example, Weber State and Utah State are both part of the Utah State Educational System. They are not simply different campuses of the same school. However, Weber State has a small campus in Layton/Clearfield. That is a separate campus of Weber State. A student that is accepted at Weber State can take classes at either the Ogden Campus or the Layton/Clearfield campus. That same student cannot take a class at Utah State University in Logan because it is not another campus, it is another institution.

By the same token, a student that is accepted to BYU-Idaho cannot take courses at BYU, because BYU is another institution, not another campus.