They do in fact verify server side that everything is where it should be. But it doesn't stop people because ultimately the inputs of a high level player in Trackmania are nearly indistinguishable from inputs of a bot playing the track.

CS:GO faces the same issue where inputs by high level players are indistinguishable from cheating.

Speedrunning tends to have similar issues, where people perform tricks that are so close to TAS inputs that it can take years to spot an issue. Or in case of Dream, it takes an entire statistics paper to explain why they cheated. In those cases it's even worse because you cannot do server side validation on video data.

Being against anti-cheat is effectively being against competitive gaming or speedrunning.