In one of my high school computer classes we'd often set up UT2003 LAN games. I was once called a cheater by someone sitting behind me who, at any point, could have directly observed my every move and corresponding input. I was baffled and amused at the same time. People that lose games have plenty of incentive to claim their opponent is cheating.

On the other hand, as my skill level increased in FPS games it became more and more obvious when one of my opponents was cheating. So IMO you can trust Magnus' ability to accurately estimate the chance of Hans cheating, but you can't trust his motivations for making the claim.

Aside: When you combine high skill levels with cheats that were designed first and foremost to avoid detection, it becomes almost impossible to do detect them. For example in FPS games "aim-bots" are crude compared to "hit-scanners" that simply auto-trigger when your crosshair happens to pass over a valid target. Combine a hit scanner with a player who already has top tier accuracy, and you get super-human accuracy. Let the player enable and disable the hit scanner in real time and they control exactly how accurate they are without any conspicuous appearances. You'd have to (externally) record and sync the monitor's output with a camera that monitors their mouse movements, and even then you'd need EXTREMELY accurate timing - most likely a capture rate higher than the monitor refresh rate.

Chess is not some random online video game though

My most pro game experience was Battlefield 2 and I'd go on a public 64 player server and score most kills with only the knife. Thing is: My team mates and other pros were capable of doing the same. No pro would accuse us of cheating, just the average Joe's.

I saw something about a runner being disqualified because they moved 9 hundredths of a second after the gun. Ten hundredths is permitted but nine is not.

It’s not impossible to believe someone could be just a sliver faster.