Watch the video. He is basically at the same height as the peak of the mountain. 5400 feet. The curvature of the earth is 8 inches per mile squared. The video includes the calculation of how much of the top of the mountain would be hidden by dropping beneath the horizon. (~770 ft). I see no problems with his calculations.
I've watched the video. If you don't know why you can see the two mountains despite the 770 ft "drop" according to the calculations, you'd really like a magic trick I used to do with my kids when I used to steal their noses from their face. Hint: it was my thumb....
Please tell me which company you work for as a scientist. I'm looking for my next "short".