Heh. Nicely put. I haven't had time to read his paper, but I suspected strongly -- if for no other reason than the audience -- he wasn't going to mention how the orbit wasn't quite as simple and perfect as that first approximation!
Right. Even nominally-geostationary satellites (the ones actively kept on station) are not
precisely stationary. They're kept within a tolerance box to avoid wasting propellant on excessive precision. Typically it's only small enough to ensure that the satellite remains within the beams of the (usually non-steerable) antennas pointed at that orbital location, and that they don't drift into the beams of antennas pointed at some other location.
This is why east-west stationkeeping is usually more important than north-south stationkeeping; also, east-west stationkeeping uses much less fuel so satellites with a relaxed inclination tolerance (e.g., for mobile communications) can have much longer service lives. The non-zero inclination of the Inmarsat satellite over the Indian Ocean through which Malaysian Airlines 370 was transmitting is what allowed analysts to determine that it most likely went in a southerly direction.
In the mid 1970s I spent college summers as an engineering intern at the Baltimore PBS TV station. This was shortly before PBS started using geostationary satellites for program distribution, starting with Westar IV, I think. When I returned for a visit, they were uplinking a program and that gave me an idea. I punched up the satellite downlink on a vectorscope (a special-purpose oscilloscope that showed the NTSC color signal in a polar vector format) and selected house subcarrier (which was being used for the uplink). This would show me the relative phase between the uplink and downlink. Sure enough, the color burst was rotating very slowly, indicating that the range to the satellite was slowly changing. The NTSC color subcarrier is about 3.58 MHz, which has a wavelength of about 84 meters, so each complete 360 degree rotation corresponded to a change in range of 42 meters.
I don't remember the actual rotation rate, but it was quite slow so the actual range-rate was only a fraction of a meter per second. In these days long before GPS I thought it was totally cool that I could measure the relative velocity of something that far away so precisely using equipment that wasn't even designed for the purpose.
Apollo used the same two-way Doppler technique to measure range-rate, but they did it at the RF carrier frequency of about 2280 MHz so their measurements were considerably more precise than mine. The same technique is still widely used today.