Reminds me of a recent event at the least well run airport in England, where I was landing a *****, on a damp runway.
Landing, I applied gentle breaking, and the bally aeroplane started skidding all over the place. Taking the brakes off, I managed to keep it straight and stop. Carefully, and using a fair bit of rudder without nosewheel steering.
I reported it to the tower. Who said something along the lines of "thanks for that, we've had a few similar reports", and then relayed my report to the next aircraft behind me with "did you hear that" but (I listened out) didn't tell the next aircraft out, nor I think change the ATIS.
Tower can clear you to land, but the Captain has to make the ultimate decision. That needs to be a conscious and deliberate decision based upon some understanding of how much the landing distance is likely to be increased by, and being clear in his mind that a safe landing is possible (or in extremis, that any other option is worse). If the braking action is reported to be poor, then the airfield have done their bit, but this is the Captain's responsibility in the end, and it's not necessarily a black and white decision beforehand - it has to be made in knowledge of the conditions.
G