Sableye shiny

Well my anecdotal evidence would prove that theory untrue, my only shiny magikarp was from a nest and right on top of a pokestop.

No idea about Sableye but I doubt Niantic would put in work to specifically code the fact that shinies cannot come from Pokemon near stops.

What would be the point?

Nope, the actual thing about pokestop-detected ones is that you cannot see whether it is a shiny or not prior to interaction, just like the overworld model is not shiny either. I have captured a shiny Pikachu and it was seen on radar before it.

My shiny Magikarp also was captured at a Pokestop and appeared on the nearby, but it only showed up shiny once I got to the catch screen.

Interesting theory. Having caught a lot I can say that the majority of mine have come from areas far from stops or near gyms. That said i have caught a handful of ones close to stops too. Not sure if they actually appeared on the radar however, because at times it can be unreliable.