Tom is suggesting Euclid geometry is not proven at distances of thousands of miles, but he's not suggesting an alternative, so all I can really do is guess at what he means and provide observational evidence that it actually does.
Support for Euclid geometry at a distance of 3000(ish) miles = The August 21, 2017 Solar Eclipse:
If geometry and perspective work the way I understand [or at least imagine] Tom is suggesting, that some how distance observes both look up at the same surface of the Moon, the Eclipse should have been visible with 100% totality from, like, nearly the whole daylight zone of the Earth's surface. (Hint: It was not)
If geometry works the way Euclid indicates, the amount of totality should recede the further away from the path of totality that you are. (Hint: It does)
In my mind it looks something like this:
[Note: I'm not trying to strawman you here, Tom, this is what I think you are saying about geometry.
If the FE perspective lines to the Moon are wrong, please provide us a diagram that can account for
A) All observers seeing the same side of the Moon
B) The same observers not seeing 100% totality of the Solar Eclipse
C) [optionally] Falsifies Euclid geometry at 3000(ish) miles]