Technically, the WWE Championship's history includes the entirety of the WWF and WCW Championships. The World Heavyweight was a new belt Eric Bischoff handed to Triple H.
Though WWE has said precisely that on certain occasions, they've also said precisely the opposite on other occasions. In their DVD on the history of the WHC (so, just for consumers who apparently love the WHC enough to buy a DVD about it), they say it begins in 1905, then became the NWA (alliance) title, then became the WCW title, then was "brought to WWE in 2002," which is what WWE.com's championship history pg says for the WHC. (Though when it says this on the championship history pg, its inherently ambiguous, cuz it could mean brought from somewhere else or brought from Eric Bischoff's asshole, who knows).
Also, in a WWE magazine issue from the last yr, in an article on the title's history, they heavily emphasize that it goes back to 1905, I remember Triple H and Daniel Bryan specifically describing it as a belt formerly held by (insert old, old names).
So, WWE is purposely ambiguous about it. Maybe once the WWE version of the WHC has been around for 20, 30+ yrs they'll say it began in 2002, but for now feel the need to refer to ancient times in order to give it significance.
Btw, I don't consider it to be so wrong for WWE to claim he NWA title's history. They can't claim that the WHC is
the NWA championship, as the NWA championship continues to be defended to this day, but they can retroactively declare former NWA champions to be former WWE World Heavyweight Champions
. WWE decides for itself who to consider "former WWE World Heavyweight Champions." Lol the NWA itself ambiguously claims the history of previous championships, and not just the National Wrestling Association (old NWA) title that was merged with their own. So, the NWA plays the same game.
The AP poll can declare a college football champion, pro football champion, pro wrestling champion, w/e they want w/o any permission from those sports' (or fake sport's) sanctioning bodies
, and thus WWE has the same right to say "Lou Thesz was a WWE World Heavyweight Champion, because we at the WWE consider him the World Heavyweight Champion in 1947. Congrats to Lou." I know this is another issue, kind of, but it certainly plays into the VALUE of the WHC. Saying that all these fantastic wrestlers going back to 1905 held the WWE WHC goes a long way in making the case that the WHC is of equal or greater value than the WWE title, in precisely the way the OP claims: its above the WWE, but a part of it currently.