300km ain't bad
How far did the analog TV transmitters broadcast back in the day?
I'm guessing (and trying to remember back over a decade), but I think we got reasonable pictures to 50 km or so, then the "snow" started to get degrade the picture. Analogue TV degrades gradually, but digital TV works almost perfectly to a certain threshold then degrades rapidly. Of course the range depends a lot on the antennas used and the terrain.
But with satellite TV, the one satellite over the equator can cover the whole of Australia around 5,000 km horizontally from satellites at an altitude of 35,786 km. Mind the dishes in Tasmania seem to aim near to horizontal.
And no, don't suggest reflection from anything within the atmosphere, it just is nothing like high enough to give that sort of range.
Of course, you might ask how do you transmit a TV signal around 40,000 km?
Most of this distance is through near vacuum which does not attenuate the signal, while only 20 km or so is in the atmosphere.