Your entire primary including all statements will be in both groups' hands. Ultimately, you need to keep your MD statement focused on why medicine and your MD/PhD discussing the research questions they ask. Research will certainly be an important part of why you want an MD, but it is not the only or even necessarily the most important part. If you're interested in both patient care and research make sure to explicitly say you want to do both. Your application needs to show passion for both.
As to which groups will bother to "cross read" that's up in the air. At many (not all) schools, the gatekeepers are the MSTP adcom. As long as there is nothing glaringly wrong with the MD-side of your application/interview, the MSTP will be an advocate for getting you in if they want you.
Did you have a particular circumstance you were wondering about?