LFAJ, there are alternative views re wet being contaminated or not.
Dispatch 'wet' could be considered differently from landing ‘wet’, due to the different data source / assumptions, particularly where the latter is published within a table of braking actions including all contaminants.

An interesting note from the previous ICAO document.
“c) Wet runway: A runway that is neither dry nor contaminated.
Note 1. — In certain situations, it may be appropriate to consider the runway contaminated even when it does not meet the above definition. For example, if less than 25 per cent of the runway surface area is covered with water, slush, snow or ice, but it is located where rotation or lift-off will occur, or during the high speed part of the take-off roll, the effect will be far more significant than if it were encountered early in take-off while at low speed. In this situation, the runway ['wet'] should be considered to be contaminated.”

Good god; there is a suggestion, in that last statement, that a pilot should use a modicum of common sense: or not to be trusted, hence the instruction.

There are grey areas. In my then airline, at home base, >3000m TORA, B757 on a 3 hour trip so about half full load, RTOW tables no computers. Runway contaminated as MED/POOR, MED, POOR. SOP = no ops if POOR runway surface. You could certainly be airborne before the POOR, but where exactly would you be at V1 and where would you STOP. Some said do a balanced field calculation using MED and see what you need. If it is <2/3 TORA then you can go. Captain said No. Night flight, all offices closed. Airport said they had no plans to re-clean the POOR. They had done all they could and achieved no improvement, especially as temp was falling.
Some said do a landing performance using MED at TOW and if that was <2/3 LDA then go. Captain said No.
Quite simply it was a grey area. Later, a B747 freighter landed, having calculated, we assume, that they could stop in 2/3 LDA. They didn't and ended up nose wheel just on the grass.
Captain had got home by then. Who's to say right or wrong in a grey area.

Exactly. Hence, since no sane responsible person would choose declare a wet runway dry, there will be nothing to prove since an adverse outcome is not likely to occur.

Should a rejected take off end in an overrun for other unforeseeable reasons, blackbox performance data would still back up the correct decision to deem a dry runway dry - regardless of what is stated on the ATIS.

Or if you are particularly paranoid, grab your iPhone at take a picture before the start of the take off roll. :p

Its NOT just the UK.
Other EU countries do the same.
We landed at a spot in Germany, that I have landed many times and know that a 747 can safely land there at max weight. The ATIS was reporting a wet runway. After touchdown and assessing the runway conditions, I told the tower that it was a dry runway. Several hours later the ATIS reported a wet runway once again after no precip. WTF??
There was one puddle on the pavement outside the white line!!!

Can we not use some common sense?

It does make a difference on whether you can get in sometimes.
Having to use auto brakes 4 for no reason on an effectively dry runway is rather silly.

This problem has been discussed for years. ATC's definition of WET is not the same as the performance engineers. We calculate performance increments due to depth of water, % of runway covered etc. This effects MOW for take off & landing not only for the weight allowed by length, but also crosswind limits. It could cause unnecessary diversions. We are interested in depth of H2O, the ATC, stuck in their glass towers, use change in colour. (is that still the case). You can get a change of colour if a squadron of swallows pee on the surface. Even damp is dubious.
For those who've operated in SE Asia I've heard astonishment when UK/EU ATC declare wet. They know what wet is. I suspect that, if the assessment and declaration from a distance is only visual, then there is some back-side covering. It is that era; cover yourself and ignore the consequences to others.
I've had this dilemma when, on a severe clear day, ATC was declaring wet x3 and the cross wind was right on wet limits, with gusts a little over. I could see the runway and it was not affected by water, it was slightly shiny and may have had some puddles after a shower. Now, the sun was beating down on it and the surface had drained to shiny. You can see how much water is there when reversers are activated. I watch a landing after ours and the spray was negligible.
ATC is a service provider to us in the chain of safe operations. We need accurate data/info to make safe & commercial decisions. The contaminated runway assessment is undergoing scientific change to try and help this outcome. Why is dry/damp/wet assessment not included in this process? After all it is about an accurate runway state determination.
In my later years I did consider that TAFs had become more pessimistic. I wonder if this airing on the worse side is a back-side covering issue?

Not sure what happens at other airports but suspect it's similar to what happens at my location...
- The Aerodrome Authority performs the runway inspections
- ATC is responsible for promulgating the surface state
If a deterioration in surface state is noticed by ATC they can inform pilots, e.g. "unofficial observation from the tower, runway appears wet wet wet". However, ATC are prohibited from providing an unofficial observation that indicates that the surface state is better than what is being reported. In this case ATC would normally contact the Aerodrome Authority to conduct another inspection.
When that new inspection takes place relies on availability of Aerodrome Authority combined with how busy the runway is.

I'd suggest, respectfully, that if you need a particular surface state to land and you know the reported state is worse then contact ATC ASAP (radar controllers can easily pass on a request for a runway inspection to the tower). That way you might avoid some airborne holding...