I may be wrong but I don't think that FBI runs a background check. To me, a background check involves work history, finanical history, criminal history, medical history and so on....
I think INS only cares about criminal history which they accomplice using 1) FP , and 2) Name matching with the names in a database (I forgot its name).
For name checking, INS needs first name, last name, and MI. If your name is unique and have no criminal history (or not in CIA unwanted list etc...), this test runs OK in minutes. But, if there is a hit, then they do further investigation, which takes time.