When I had DCS, the hospital took all my insurance information, including DAN. I had to fill out a form for DAN. I had two days of treatment. DAN is supplemental, paying what the primary insurance does not cover. My insurance probably sent me a breakdown on what was paid, and my wife probably looked at it. I just know I didn't pay a dime.
But DAN does more than make the payments. It is important to understand that not every hospital has a recompression chamber, and many hospitals with recompression chambers will not treat divers (believe it or not). When I did get DCS, Duke Dive Medicine of ScubaBoard (who is not DAN) did what DAN would have done if I had called them instead. He told me to go to the hospital, he told me what hospital to go to, and he told me the doctor who would treat me had been advised that I was on my way.
When my diving buddy had symptoms while in Cozumel, DAN told him to go to the chamber, and they told him where to go. When I started having unusual symptoms an hour later, the same guy at DAN told me it didn't sound like DCS and didn't advise me to go. (It turned out to be Covid-19.)