Rule #1 about pre-med advisors/committees: YOU are responsible for checking on the admissions requirements and making sure THEY are doing what you need them to do (if you need them at all). Don't make the mistake of taking everything they say as law of the land without double-checking the admissions requirements. I recommend you read through the Osteopathic College Information Book, found here:
http://www.aacom.org/resources/bookstore/cib/Documents/2014cib/2014 CIB Complete Small.pdf. Letter requirements are listed for each school.
As for your inability to shadow your research mentor, that's rough! I agree with Jedi. Your research mentor could certainly be the stronger letter, but if you're applying to DO schools I would try to shadow a DO and get a letter. How have you contacted the DOs in your area? Maybe you can ask your pre-med advisor for help finding one in the area if your school keeps lists on physicians known to allow students to shadow. If you absolutely cannot find a DO in the area to shadow, then you can try shadowing a practicing MD. Just keep in mind that if you have a MD physician letter you cannot apply to the DO schools that require a DO letter.
Try sending Goro a PM. You'll get a better answer.