He's clearly not a physicist. A physicist would understand that just because the stopwatch has extra digits on the right doesn't mean it's actually measuring it to ±0.01 seconds. Human reaction times would make it ±1 second at least. Without the stopwatch being calibrated against a source based on an atomic clock (like a GPS receiver) beforehand, you can't even guarantee ±1 second precision.
Likewise, measuring it "at a station" also impacts the precision of timing measurements - is the stopwatch clicked when the station comes into view, when you pass the start/middle/end of the platform, when you pass a sign on the platform or just some random point somewhere in the rough vicinity of the station? How precise is the distance given to the relevant point, is it just in miles and chains (i.e. ±20.12 metres) or is it accurate to the nearest metre? Is the exact track to be followed the source of distance measurements, or is it some approximate distance applied to all tracks on the route?
A physicist would understand that the various errors in precision (stopwatch calibration, inaccurate distances, inconsistent measurement points, reaction times, calculation mistakes such as imprecise conversion) are all multiplied together, not added. I've just done a few quick sums and found that you're dealing with potential errors of anywhere between 2-6% on a given interval from one station to the next, easily enough to account for pulling a figure like 129 mph out of the air.
Without having a motorsport-style transponder on the train and timing beacons placed at locations previously surveyed for the exact distance on the track path to be used, you can't expect to get anything within ±5 mph for the average speed over a given interval, especially not distances shorter than about 10 miles. His accuracy claims are not to be taken seriously.
I'm actually a biologist (and a bit of a motorsport fan) but I do not claim to be
that accurate, just lucky, hence the word 'somehow'. I was doing my absolute best to keep within 0.25 seconds of accuracy, but was only able to do station-to-station times because I was on the wrong side for the mileposts. The 0.25 seconds came from a combination of practice (i.e. doing this a lot) and quick reactions (I've tested quicker than 0.2 seconds before). The figures usually given are either the centre of the platform, the station building or a nice noticeable point like the footbridge (and most milecharts have a note to say what to look for). Miraculously hitting 0.01 seconds over a nearly 4 hour period was pure, blind luck.
I also tried to callibrate them by looking at the figures on either side. Taking
City of Truro as an example, I would consider the 102.3 mph to be unconfirmed, because it was not backed up by (for instance) 100 mph on either side to allow for fluctuations. Same goes for my 129, that was not confirmed (flanked by 116 and 108). My 127 on the other hand was, since that was flanked by 126 and 124, themselves flanked by 121 and 120. That could be interpreted two ways. One, random fluctuation. Two, the train speeding up from a speed restriction (110 north of Bletchley) and peaking at a speed just beyond the speed limit, then slowing down again (for the 115 north of Bushey).
Another point is the length of the train. I was in Coach C, the seventh vehicle. I checked my log against John Heaton's. He was one of the official timers, in Coach J I think, but had to allow for the 375 ft or so of train between us. It turned out to be remarkably close. He actually got 128 at the same point I had my 127, but was obviously on the other side and working from quarter-milepost.
Also, remember, each individual point is independent of the previous one. Unless the watch itself is wrong - and I ran it against the Speaking Clock beforehand - then there are a series of individual possible errors rather than a cumulative one.