That does indeed assume a sphere. If you are curious about the geometry, maybe https://en.wikipedia.org/wiki/Horizon#Distance_to_the_horizo... can help.

If you run the calculation the other way around, every satellite has to service a ground patch with about 380 miles radius. And your antenna has to swivel to a point that might be more than 60 degrees away from zenith. So every obstruction of more than 30 degrees above the horizon will lead to at least intermittent disconnects.