You are confusing a speed record achieved with by a highly modified (i.e. larger wheels, stronger engines, very few car between the locomotives) train on a specially prepared line (strengthened tracks, increased voltage in the catenary) with approved operational top speeds during normal service, for the TGV that would be 270 to 330 km/h (170 to 205 mph), depending on the layout of the line.
Surely HSR trains will not stop at every small town, but if, say Pennsylvania is expected to subsidise the construction of an HSR line through the state they will demand at least one more stop between Philadelphia and Pittsburg, namely Harrisburg. And there's no way you can build a network of HSR lines without subsidies, at least it has not been done anywhere yet.
An average of 300 mph in normal service is completely impossible with conventional trains, the wear and tear would be excessive (on the record ride of the TGV mentioned by you the collectors sufferd heavy wear, emitting a lot of sparks above the speed of 300 mph). You would need friction-free MagLev technology to achieve such a high average speed.
Granted I did so. However, note that OTL, maglev trains are already in operation and that JR is set to have a maglev shankansen in operation between Tokyo and Nagoya by 2025. ITTL, I would expect more funding going into R&D for maglev earlier. Even if it did not, trains already exist OTL with
average speeds in excess of 200+ mph (see
China's CHR - average speed 217 mph), so an average of 200+ mph
is most certainly doable.
As for stops in every little town, note the statement wasn't that trains won't stop in every little town, but that express trains won't do so. Yes, there will be in the "little towns" like Harrisburg, but I certainly wouldn't expect every train to stop there. That's why there are locals, expresses, and various flavors therof in the first place.
To take the example of the shinkansen, the one I'm most familiar with, there are 15 stops between Tokyo and Shin-Osaka on the Tokaido line. The Nozomi (fastest express) stops at 4 of them, while there are "semi-fast" and locals that make more frequent stops. I would expect similar service in the US, or even less. I could easily see the fastest expresses for the example of an NYC-SF route stopping only Chicago, Omaha, Denver, and SLC, while the next fastest stops at Philly, Pittsburg, Cleveland, Des Moines, and Sacramento as well, and then a level of service or two between that and the locals. (I could even see a super express non-stop, although that may be a stretch.)
All in all, I still think a 300+ mph average speed HSR network is doable by 2010 ITTL.