To my knowledge, the only legitimate academic degree available in martial arts offered in the United States is through the University of Bridgeport (click here) with their B.A. in Martial Arts Studies program. In addition, as they are Olympic sports, some colleges offer scholarships for sport Taekwondo and Judo, but do not offer degree programs for these arts. Everything else you see in the martial arts with regards to "academic" degrees ranges from conversation pieces to outright misrepresentation. The difference, in my opinion, comes down to how such piece of paper was obtained and how it is used. Is it something you were ceremonially awarded, or something you consciously applied and paid for? Is it a footnote in your resume along with other honorary awards or are you calling yourself "Doctor?" Unlike martial arts certifications, there actually is a universally accepted standard when it comes to academic degrees. So like anything else, the legitimacy of having such all comes down to what you claim.
That said, I do not think any serious martial artist takes these degrees as anything more than what they are. When I read about someone having one or see it on their wall, I say "cool" and move on. My own teacher has one in fact. However, as any sane person does, he calls it what it is: something nice given to him by someone as a gesture of respect. In today's world, acknowledging respect is something we need to do more of and encourage.