This blanket statement is not true. I'd go out on a limb to say most laypeople (i.e. the vast majority of patients) would assume that the DO introducing them self as Dr. So-in-So in a clinical setting was an MD anyway. My mother went to an allopathic school and in her practice there are DOs; she claims that the difference in clinical prowess among the physicians in that practice vary based on the individual, not the letters behind their name. Most people don't know who is treating them. I've watched patients continue to refer to the PA as doctor despite the PA having corrected them multiple times in the same conversation. With this in mind I'd bet the patient refusing to be treated by a DO to be the exception and not at all the rule.
Those matriculating into osteopathic schools have lower stats on average than their allopathic counterparts, we can all agree on this. But your statement, bolded for emphasis, is based on the assumption that stats alone dictate the caliber of future physician. If this were the case DOs would not be eligible for allopathic residencies. Are they at a disadvantage for these residencies? Yes. But would they be allowed the opportunities to attend them if the governing bodies deemed them inferior? I don't think so.
If you really mean this I think you're in for a rude awakening. Lots of people respect docs and a lot of people don't. For everyone who looks at you starry eyed like you're some mystical healer there will be an equal amount who think you're overpaid yuppie who doesn't know what they're talking about. One of my neighbors' son recently broke a stain glass window in my mothers house. When she asked that family to pay for the damages they said "you're a doctor why they hell do you need our hard earned money?". She's also received numerous insults and death threats (she practices in Baltimore) by her patients. You may think you're a big deal for having gone to medical school but many do not feel the same.
