If you think logically for a minute, if a patient has NO idea what a DO is, why automatically assume it must be inferior to an MD? Couldn't it be possible that same patient can just as well conclude that the DO is an advance degree that MD take? (MDs are dime a dozen, DOs are more rare. Look in the phone book - it is not an illogical conclusion to assume a DO is an MD with advance training or something - this is assuming no research on "what is a DO/osteopathic medicine" on the part of the patient)
Also, since when does not having an MD stop people from giving advice. Your family members give you medical advice, that teenager working behind the counter of GNC is giving health advice, the informercial guy selling you an all natural colon cleansing product is giving advice ... the lovely lady wearing a white lab coat in Sheshido is giving nice derm advice ... and the public buys it. (spend enough time in the hospital and it seems people take everyone's advice EXCEPT their doctor's advice)
Also the wait time for specialists/referrals is several months. If a particular patient doesn't want to see someone because he/she is not an MD, hey ... i doubt the DO specialist will ever notice. And if you're located in a more rural area and that DO specialist is the only specialist within 50-100 miles ... well, it's the patient's choice.