I think some posters are missing the point. It's not that people "believe in the Jones counter." That's like saying "I believe in my steel tape/in my theodolite/in my ****."
The only thing to "believe" about your measuring device is that if you use it correctly, you'll get a measurement that's accurate to within the limits of your device, and repeatable.
The Jones Counter is nothing more than the "readout." It reads out in an arbitrary count that's directly related to the circumference of the bicycle's wheel. My old Jones Counter used to read something like 47,000 counts per mile with the rims and tires I used to use. I have no idea what the newer ones read out, but it's unimportant -- the point is that each "count" represents a very small distance.
It's the PROCEDURE that's crucial!
It's been mentioned but evidently needs to be mentioned again.
1. record what your device "reads out" as the length of a distance THE LENGTH OF WHICH IS KNOWN AND IS TAKEN AS ACCURATE. This is always a straight line, measured by a different "known-to-be-good" measuring device. This "calibrates" your bike, meaning that you know, within tight limits, just how many counts on the Jones Counter will measure a mile (or kilometer), on that day, at that time, in that place.
2. measure the race course, using your just-calibrated counter.
3. return to the course of known length and observe the difference between what your device read out the first time, and what it reads now.
4. adjust
Doubters/complainers -- the whole point is that this is standard practice everywhere in the world of measurement, not just in road race courses. It's true that with many measuring devices (think micrometer, for example, or digital voltmeter) the calibration, once done, won't be redone for some time. With course measurement the recalibration is done immediately. This has nothing to do with the Jones Counter itself -- it's just the readout -- but has to do with the known/expected slight change in the circumference of the bicycle tire.
If you have a digital camera or camcorder and have ever adjusted your "white balance," then in effect you've done a calibration. If you've been around a while and have used an "18% grey card" in b/w photography, you've done the same thing. The standard video "bars and tone" is meant for calibration. Calibration/recalibration is everywhere.
I've measured XC courses and laid out short training distances in parks with a surveying wheel. A surveyor's wheel is a useful tool but it's in a completely different measurement world from the surveyor's other instruments and from a calibrated bicycle measurement. When I got my first wheel, back in the seventies, I immediately calibrated it on the calibration course. It was 9' long per mile and it kept changing as the rubber wore down. This is normal, and expected. It's a property of the tool, and it's not a good enough tool for road race measurement. It may be called a surveyor's wheel but you'll rarely see a surveyor using one. Mostly they are used by construction people -- roads, bridges, etc. -- where it's just the right tool for many measurements.
I love GPS devices. Other posters talk about the positional uncertainty, which can be as small as 10 or 20'. The thing is -- that uncertainty is always changing. If the device is only receiving 2 satellites, then it's high and it can't even attempt altitude. Most modern GPS receivers are 12-channel and when they're receiving signals from half dozen or more satellites the position uncertainty is very low. When the satellites are low in the sky it's high. When they are close together, it's also high. When they are well-placed from an angular point of view, it's low. And so on. My point is that it's always changing because the satellites are in motion and they have different orbits. This isn't a secret.
If you have a hiking-style GPS unit (rather than a wrist one, which doesn't usually display the actual positional data) then take it and put it down somewhere and watch the display that shows your positional uncertainty. It's going to change while you're watching. Switch to the display that shows how many and which satellites are being received -- this is most easily seen on startup, as the receiver tries different channels. You'll see the uncertainty change as more signals are received (or lost), as satellites low on the horizon come in, those high in the sky come in, etc. etc. That's always going on. That's how GPS works.
So, again, measurement people only "believe" in their basic method, which is a standard method, widely used.
Oh, and I should say that of course there are sloppy measurers, measurers make mistakes, and so on. You can put an excellent tool into someone's hands but that doesn't mean that he or she is going to use it properly.