André, I think you have found the source of the early part of this line on Geni.
If you click the parent links on each profile, you can construct the following claim:
Werner II was son of Heinricus von Rheinfelden, of Schauenberg
Heiniricus was son of Werner I
Werner I was son of Konrad
Konrad was son of Konrad von Zähringen and an unnamed daughter of Berthold von Uesenberg.
I have some familiarity with medieval genealogy in Bern but I'm not an expert and I can't judge the quality of this line.
Werner II seems to be well-sourced (Rübel-Blass) but the other generations cite only "Rudolf Franz Kindler, Ahnentafeln, Lörrach 2000". On a quick Google search, the only information I find about Kindler is a 2004 death notice in the journal of the Genealogisch-Heraldische Gesellschaft Basel.
Moreover, a note on Werner II says, "In RB [Rübel-Blass] not indicated whether same family as the Burgundian family of the Counts of Rheinfelden".
I think it would be reasonable to conform the line on Geni to this source (pending further research), but I have reservations about keeping the connection to the Zähringens or restoring the Uesenberg connection.