Degree /= Credibility
I think the statement "Degree = Credibility" is one of the biggest mis-sold pot of gold at the end of the academic rainbow.
To many employers, a degree assists in proving your credibility, but doesn't however equate to credibility itself.
Ways to lose credibility are to turn up late to interviews in a pair of jeans, unclean shaven, have no pen and pad to take notes and have no knowledge (even at a fundamental 'what does this company DO' level) of the employer for whom you're hoping to work. Get ALL of that wrong, and no degree in the world will help you! :o)