There is normally no insurance mechanism in place to reimburse non-retiree veterans who seek care in a civilian health facility. (There are some limited exceptions for recently discharged Vets)
That's why the VA has a complete, stand-alone healthcare system. When it was first thought of (1930), that was the most cost effective way of doing it....plus, that was before health insurance was common. As Guest 11/10 pointed out, the original intent was to take care of former servicemen who had injury or illness incurred as a direct result of their service.
On the more cynical side, like most benefits (though this one is certainly deserved by it's recipients) this one has become a political golden apple. Once the VA was there, no one was going to dare take it away. All they would do is make it bigger and grander. The number of veterans is staggering and if you do anything to "help veterans," you just locked up a huge block of votes.
Unfortunately, the second aspect sometimes interferes with the first. The politicians get TOO generous. If you visit the VA website and see who rates care at a VA facility, you will see a list of categories and levels that approaches the complexity of a space shuttle launch. That's because politicians, seeking to garner favor among vets, have expanded health coverage well beyond its original intent.
For example, if you are an indigent, homeless drunk who did one hitch in the military thirty years ago and never left Fort Hamilton, you can receive treatment for your alcoholism at the VA. That was never the intent of the system, and the simple truth is that that guy takes space and money away from a vet with a true, service connected health problem.
Though I vote for him, McIntyre is the King of Pork, and this is just his standard M.O.
Two additional factors, WilmMAJ