Seal Team 6 are Tier 1 which means their chain of command bypasses everybody and starts at the top. Which means barely anybody in the govt knew about the operation. This isn't something that is going to have multiple sources to verify every little detail. To view the media's reports as reflective of the people who are actually in charge of seal team 6 getting their stories mixed up is silly.
I'm not sure why you needed that explained to you or what kind of jump off point that is for anything.
Normally, they report to Joint Special Operations Command at Bragg. And under normal circumstances, even DEVGRU (Seal Team Six) would report to the theater commander (CENTCOM) when operating in the CENTCOM area. BUt this was not normal circumstances. I wonder if CENTCOM was even aware of what was going on?