From the organizations that I'm familiar with, the problem is that he is matriculated at a 2 year community college (rather than a 4 year college or university) and not that he does not attend the college or university where the chapter is chartered.
There are organizations that allow certain chapters to accept students from other schools (not to be confused with core chapters and citywide chapters). There are also chapters for some organizations that are allowed to accept graduate students.
I say that the organization knows better than outsiders do.
That's with the assumption that the student and/or chapter did not lie on the paperwork. That also happens, unfortunately.