I got in the system though I was stateside during the Korean War and did not have to prove it was service connected. I do pay a reasonable co-pay each time I go to the VA hospital. If I see several doctors on the same day, it still counts as one co-pay. And I did not know anybody at the VA.
There are eight priority groups determining eligibility into the VA system… In my Veteran’s Health Benefits Handbook, which discusses my specific eligibility, Enrollment Priority Groups is on pages 7-9. The various priority groups include various service connected disabilities, former POWs, veterans awarded various medals, veterans who served in certain specific wars, actions, etc., veterans with incomes below the geographic means test, and so on. So if the information in my Handbook is still in effect–my Handbook is some four years old but is undated as far as I can tell–there are numerous rules, some more than a little complex, determining eligibility.
Again, the only way to know if one is eligible is to apply. One should let the VA determine eligibility.