There is definitely data that supports the fact that DOs aren't treated the same as US MD. Here is the 2014 program director's survey report:
http://www.nrmp.org/wp-content/uploads/2014/09/PD-Survey-Report-2014.pdf
Many programs just won't interview/rank DOs in the more competitive fields. For example, in neurosurgery only 21% of programs interview/rank DOs while 96% of programs interview/rank US MD students. And here is the kicker, you have a better shot matching into neurosurgery from a caribbean school (40% of programs interview/rank IMGs). However, the opposite is true for almost all other fields (where more programs interview/rank DO than IMGs).
I think it is also time that I introduce to you the concept of the non-LCME filter that PDs use. PDs have filters for various variables when looking at candidates this includes board scores, region, and yes even DO status. Let say you had a USMLE score of 270 as a DO. If a PD were to put a DO filter when looking at applicants, it is as if your application never existed to begin with! So they would have never seen you get a 270 at all, since your application was filtered (like GPA or MCAT filters that DO schools use). This is what eradicates DOs from the US MD pile and the strongest contributing factor to DOs not matching into ultra competitive specialties and top tier programs.
I'm not even getting into the MD = DO + 10 on the USMLE aspect either...
Yes, there are many other reasons why DOs are not selected (ex. no specialty specific research, lack clinical rotations with residencies, no excellent LORs from big shot physicians). However, don't think for a second that their isn't a DO bias even when you have the full package.