"very questionable" answers your question. Rush likes to deal in facts, not questionable suspicions. I totally question Obama's background, but without proof, it is an unprofitable argument that won't win over a single liberal.
But...Are you a close friend of Rush that you would know?
I only know the facts. He rarely calls “liberals” what they are ( Fascists and Marxists). In the past few years he has moved toward using the words, leftist, progressives, and ( rarely) socialist.
He spent little time on Obama’s lack of background, or fake documents, fake Social Security numbers, and other questionable aspects of his background that are **known**. ( Ayers, Wright, Marshall, etc.)
Why does Rush do this? Your speculation is as good as mine. I speculate that there were threats and possible blackmail. Perhaps, in time, Rush will tell us.
Finally.... I admire Rush and am grateful for him.