Thank you for your reply. It does look like the VA is finally accepting the fact that they have to pay for this necessary ER visit to a private hospital. This VA webpage ( http://www.nonvacare.va.gov/emergencycare.asp
) explains it fairly well.
I was dealing with the billing department in a large VA hospital, the private regional hospital's billing department, and the billing department of a ER physician's group headquartered half a continent away. None of them would admit that the VA had to pay.
It turns out that I needed to be dealing with the "Control Fee Unit" (CFU) in a VAMC in a different state altogether.
Once I found that unit then everything became simple. I was told to send the bills and a short statement to them about the reason for the ER visit... then they would handle everything. They said there was no question about the VA paying in this situation. Just like with a heart attack... you cannot delay getting treatment for a stroke.