You're taking it waaay too literal. Vectored thrust will let it make sharper radius turns, but it isn't coming to a stop and changing direction 90'.
That’s a picture of a Harrier from the side during a vertical landing. FLIR is FORWARD Looking Infrared and the plumes would be hidden by the Harrier’s wing.
They object they track (while they are in a turn) rotates and never shows exhaust plumes.

The chase plane said square corner, so it’s a square corner. He wasn’t the only one who’s seen it.
Your second point makes no sense.
The point is that I can re-create 1890s level of UFO capability with about $2M today, and I can re-create vectored thrust boundary layer control UFO Capability using 1947 technology.
Occham’s Razor forces an inductive conclusion that these are secret projects.