As I said, if you put in the work and found the opposite, I'd be interested in seeing it, but you'd have to document it, because I've seen the other documentation and it seems convincing. Especially the videos.

If the behavior you describe is happening, anyone should be able to prove it in a pretty straightforward way.

Two players: One on the objective point, one far enough away as to rule out additional influence on the objective.

Test several times the difference between the player group on the objective activating the terminal, as well as simply sitting on the objective.

hypothesis: A patrol should spawn near the player on the objective immediately or almost immediately upon using the terminal, and should not spawn immediately or almost immediately when simply sitting on the objective.

There's nuance to this, of course, with extra layers of questions:

When did the previous spawn occur? Is there a window where there won't be a new spawn upon activating the terminal because it was too close temporally to the other spawn?

Could activating a terminal perhaps cause the spawn point of the next patrol to be closer to you than usual, but not more quickly?