I contend there is to much atmospheric distortion for triangulation or parallax to be used for this purpose.
Not very good with optical geometry are you?
At avery simple level, if your assertion was valid there would be a marked difference in star positions when you change altitude or are in places with exceptionally dry air, like Death Valley.
Clarity increases, but star positions stay the same.
And a star map would be useless, unless it was made for the particular hour you are looking up in the sky. You could not just rotate the chart to the correct hour and location, the stars would be shifting all aver the place if atmospheric distortion operated at the level needed for the FE explanation of parallax and the horizon affects. A half decent amateur astronomer can calculate the positions of stars that he can not see with his naked eye, if there were major shifts as they come up the arc of the sky, then they would know.
Even the primitive star maps and telescope I use with my kids would be useless.
A telescope can prove you see funny looking airplanes in the sky, but they can't prove that what you're seeing is a satellite.
Actually, since most satellites are not aerodynamic, lack wings, and have no visible exhaust, they can neither be rockets, nor airplanes, and the altitude is too high for balloons.