This thread is more interesting than a hog chasing it’s tail. :D I do find it interesting that it seems to be opinions vs facts with sources.
I spent a bit of time looking for sources via google but found more opinions. Here’s one from a tire place for RVs.
https://www.lesschwab.com/article/how-to-avoid-or-repair-a-flat-tire-on-your-rv-or-trailer.html Curiously, they didn’t say where to place the bottle jack.
I think any instructions should be for an RV etc. Otherwise, the instructions could be for an unloaded truck. Fyi, I did find one post on Ford Trucks site that said don’t put a bottle jack under the differential.
YMMV.