With all this conflicting info, I'm confused and I've shot perhaps-hundreds of these
Well, yes, according to your "rules" you are confused.
1. A tripod is not generally necessary for wide-angle panos. The confusion may come from the circumstance, that wide-angle shots, particularly in portrait orientation, include close areas at the bottom of the frames. This may or may not pose a problem.
Demonstrations:
a. Scenery:
Lake Louise Fairmont ChateauHand held at 17mm (*1.6), portrait. The result on the pavement is in the attachment. This type of error is difficult to clean up, the solution is often cropping.
b. Scenery:
Vermillion RiverHand held at 17mm (*1.6), portrait, standing on a very low, tiny bridge, but that distance was already enough to mitigate the closeness. There is no problem with the stitching.
c. Scenery:
Paint PotsHand held at 17mm (*1.6), portrait. There must be parallax errors on the ground, but I did not notice them.
2. A "ball-head" does not allow for horizontal rotation. The rotating base does, which may or may not be part of a ball-head.