There is a difference between your university having affiliation with a Spanish University and your university having a program at a Spanish university. Those who study Spanish at UCM go through a program sponsored by a university. Those students have the option to take classes with fellow program members or do what your university does, allow you to enroll in classes with other Spaniards, hence the higher level requirement. Do a search on studyabroad.com (I think that's the link) and find programs offered at UCM. Another option is Univ. Antonio de Nebrija
http://www.hispanicosnebrija.com/spanishcourses/, a private univ. in Madrid. They have classes you'd be able to take with (although once again, you'll most likely be with other foreigners without an advanced level of Spanish).
Now, here's another question- will your university accept the credits for not going through their set up? That's something you'll have to find out (unless you don't care about receiving credit).