There seems to be a concern that claiming disability benefits may jeopardize one's FAA medical. This is not true.

If one claims disability benefits, this does not impose any burden on the FAA medical: the FAA does NOT make aeromedical decisions based on disability claims. Failure to report disability claims is a violation, however.

If one has a condition that does not meet FAA medical standards, this imposes a burden on the FAA medical. It doesn't matter if that condition arises from military service, a bad divorce, or the stressful world of Shakespearean sock puppets. If a medical condition exists that requires further scrutiny (special issuance, testing, documentation, etc) for the application for an FAA airman medical certificate, the FAA considers that condition, and the person with that condition, on an individual basis.

The concern seems to be, "can I hide this from the FAA?" If one is concerned that making a military disability claim might interfere with FAA medical certification, one isn't concerned about the military claim, but rather being caught with someone that one has elected not to reveal to the FAA. This is a violation; failure to cite a disability claim is a violation, but so is witholding information for the FAA airman medical application. Furthermore, exercising the privileges of a FAA medical certificate, while not in compliance with the FAA medical standards, is a separate violation every time one exercises those privileges (five legs in one day is five separate violations).

One can grouse all day long about the unfairness of FAA medical standards, but these standards are what they are: well-established aeromedical standards with the authority of a federal administration and an Act of Congress to back them up. In the context of revealed conditions via application for military benefits, the issue isn't unfairness to military veterans, but ultimately an issue of an individual who is either caught, or doesn't want to be caught, with an unairworthy or non-compliant aeromedical condition.

These lines of conversation tend to overlook the underlying, and most important element: if one has a condition that does not meet FAA medical standards, one shouldn't be flying with that condition, and one shouldn't hold a FAA medical until that condition has been addressed satisfactorily. If one has a disqualifying medical or mental condition, one should absolutely NOT be flying until that condition is resolved. One is absolutely NOT legal to fly until that condition is resolved. Whether the condition is resolved by treatment, or by testing and documentation adequate to demonstrate compliance, it must be resolved; one who whines because (s)he is revealed in deception, in an effort to hide a disqualifying condition, has no leg upon which to stand.