How would you guys feel if an MD wrote DO after his/her name? If you are arguing they are the same, there should be no problems doing so; however the OMT and other factors make the two different. As the philosophy of training is different, so they should be distinguished as a part of the title.
Think of it as 2 routes to become a physician....either MD or DO. If a patient asks, all you need to do is say that there are two ways to become a doctor and that DOs are trained in OMT and MDs are not. It doesn't usually require more explanation than that. Think of undergrad: you can get a BA or a BS degree (among others, like BSN, but you get my point)...why list it as the other one? They are similar, but have different requirements.
One point, however, is that it is law in my state, and undoubtedly others, to represent your actual degrees and certifications. They will suspend or revoke your license if you state you have one degree and actually have another, or say you are board certified when you are not. It reflects on your character and integrity to be honest as to what your qualifications and achievements are.
The hospital I trained at distinguished MD/DO/MBBS/NP in the paging and physician directory. If a glitch in the system gave you the wrong label, it was something that would be end up getting corrected (at least once the EMR was up and running and other more crucial problems were fixed first). The guy who was an MBBS in my program signed his scripts with MBBS behind his name. The issue is how you represent yourself; if the computer thinks a DO is an MD, then that is a system problem....if a DO states he is an MD, and writes MD behind his name, that is misrepresenting training and is answerable to the powers that be.