I ended up self-paying for my surgery after insurance denied me, several times. In order to file with the insurance company, I had already jumped through all of their hoops, including the psych eval, and 6 month supervised diet. I can honestly say that the nutritionist who did my "supervised diet" was not very helpful, I learned much more in the one visit with the nutrionist my surgeon recommended! (But that's just my personal feeling).
Also, I will say that I had a hiatial hernia (as discussed in your book), which was not detected pre-op, but it was repaired, even though I was a self-pay patient!
I think it really depends on the surgeon and the program they're associated with. And not as much whether you self-pay or go through insurance.