All the stuff post-WCW lineage (except WCW TV-where did that come from) I agree with, as that was all merged with the IC then merged with HHH's belt. But, Jericho unified the WWF and WCW belts to create the Undisputed title, then HHH won it, then Hogan won it, then Undertaker won it, then Rock won it, then Brock won it, then Big Show won it, so forth. Why would HHH get half the belt for no reason other than he wanted it (in storyline terms)?
Basically... HHH was the last person to wear the Big Gold Belt...
When he won the Undisputed Title from Y2J, the next night the current WWE Title was given to him in exchange for the other two belts.