The GWR services that have cycle reservations have woefully poorly designed cycle spaces that are indeed too small to fit some normal road bikes! I tried to travel with mine once; it wouldn't fit in the "proper" way and I had to position it awkwardly sticking out of the cycle compartment and slightly blocking the exterior door, and then remain in sight of it for the whole journey in case anyone needed me to move it! Fortunately as it was a relatively short journey on a quiet train, nobody did.
However if someone turned up on a much busier service with a bike too large for the space, it could cause trouble, and of course actually putting some effort into the design of cycle spaces so that this sort of mess doesn't happen in the first place is out of the question, so a silly policy like this is left as the only solution.
The measurements chosen are a little odd though - as well as being extremely small (far smaller than the largest bike that would fit on an IET), I recall the issue with my bike was actually that it was too long to fit vertically in the space as designed, not that the wheels were too large or the tires too thick.
I doubt anyone is actually going to measure it. Its probably to discourage people with those huge oversized tyres etc.
They might not measure it but I imagine this policy is to allow them to remove bikes that are obviously too large for the IETs' (inadequately designed) cycle spaces.
