I am a veteran and have never had anything denied because of expense. This has indeed included an MRI to find out why my arm continued to hurt despite nothing found on xrays.
Granted, the VA hospital in Fresno, CA is probably one of the best, but that is in large part because staff worked for over twenty years to change and improve it. They also had help from various veteran's groups.
If care in your area is not the best what are you doing to improve it?