That is exactly the opposite of my experience personally, and when I handled medical billing for my father too (end of the 90's).
I see the Dr, or hospital charges, then I see the "approved charges". Approved is always lower and the medical practice eats the difference.
My son is uninsured, a recent test was billed to him at $150, he mentioned it to me, I dug around in my records and found the exact same test I took. The approved amount was $64.72. So we took that to the billing dept - no joy, a lot of run around, but the charge remained. This test was not in isolation, there were other charges too and the total bill was in the thousands. After a lot of hassle we got it reduced to about 75% of the original, but since he does work there was no help from the low income government agencies or the indigent relief agency either.
As far as billing, it is electronic now. The medical practice bills the insurance electronically, and if you have a secondary insurer it goes to them automatically too after the primary pays their portion. Most of my Dr.'s do the billing right in the exam room on a lap top while I am there and we talk. But even those who don't do it that way, I see the EOB from the insurance company shows date received and date of service, at the most it is one day apart.
I do not live in a major city either, population is around 20K