A flat disk that is accelerating straight up would have a uniformly thick atmosphere, and the only perspective the sun would have is that similar to the person looking straight down at the clear water.
I think you misunderstand their model. Their atmosphere is still a thin layer of air on the flat disc, and at sunrise/sunset you are still looking at the sun diagonally through more air than at noon when you look more vertically.
No, I understand it perfectly. The angle described would only increase the amount of atmosphere light travels through very slightly. That total distance would be on the order of 125,000 feet total. Not enough to filter out the blue spectrum of light.
In reality, when the sun drops to the horizon, the light travels through hundreds of miles of atmosphere before reaching my eye. I say hundreds of miles, because I am a pilot, and when I typically see these sunsets/sunrises, I’m at 40,000 feet above sea level.
Another note. As a pilot I often see the sun set, then raise, then set again all within a 60 to 90 minute time frame. You see, as we approach a destination at the time of dusk, we descend toward the earth. This brings the visible round earth horizon closer to my eye causing the sun to drop behind the horizon (sunset). Then, we offload our passengers, load new passengers up, and take off again. As we climb, the visible round earth horizon moves further from my eye and drops below the sun (sunrise). Ultimately the sun sets for good during that flight.
This setting, then raising, then setting again is not possible on a flat earth.