Being paraplegic or quadriplegic does not preclude a person from being a fine physician.
I don't know, if you can't use your hands, the only thing you can do is take a history. You can't conduct a physical exam, do a lumbar puncture, start a central line, suture a laceration, intubate a patient, or put a pathology slide under a microscope. It seems like you'd be limited to being a psychiatrist or maybe a radiologist, and like Franz said (and was excessively dumped on for), you wouldn't be able to fulfill the technical standards to get to that point.
It's a feel good story when someone overcomes all that to reach some lofty accomplishment, but there is the very real concern of patient safety. There's plenty of skills that are up to the doctor to do that a quadriplegic just can't do. When there's thousands of applicants who are qualified and able to do the tasks required of them, why take someone who can only physically do a minimal amount of the work required?
And as jbar said, hospital rooms are tight quarters. Even rolling a patient in a wheelchair to a bed typically requires rearranging some furniture. It can be a pain doing it as a physically fit person. It would be a nightmare if you were the one in the chair yourself. It would slow you down, and your fellow residents and students are going to have to do more work as a result. I'm not sure that hiring a PA to do your hands-on work, or having an extra resident or attending around qualifies as "reasonable accomodations."
I don't think it would be offensive to say that a a paraplegic can't be a construction worker, or that a quadriplegic can't be an electrician. I don't see why it's so offensive to raise those same concerns when one is trying to become a doctor, where people may live or die depending upon the abilities of their physician.