I wondered what the heck a "true" saddle was supposed to be, but it looks like they roughly defined it as a treed (wooden frame) saddle with stirrups attached.
I can't seem to parse whether the tree came before the stirrup -- it's implied but not stated -- but it looks like a single mounting stirrup was invented before paired riding stirrups. I've seen a Native American (Cherokee? IIRC dated about Removal Time) saddle that was basically just a tree, presumably used with blankets above and beneath for comfort, without any indication of rings for girth or stirrup attachment, but that doesn't rule out looping them through the gap between the tree bars (where the spine floats underneath).
It was/is a trend within the last decade or so to use a treeless saddle for more "natural" horsemanship (whatever that means), and I'm sitting here wondering what that means for stirrup attachment. Layered on top of the girth, I hope, for stability. Gonna go fall down the google-hole.