People love to parrot this, but it's not true and makes no sense for them to try and game the system this way. The mandatory compensation and bad press from cancelled trains is way more costly on them than having poor punctuality statistics.

The reason that a late train can sometimes be cancelled is to try and stop a cascade of delays from happening. Tracks only have so much capacity, and if train gets delayed into a time-frame that is highly congested, trying to fit the delayed train into that time-frame will result in delaying other trains, which could then cause further problems down the lines and throw the entire network out of order.

They accept a certain number of cascading delays like this, but sometimes it's just known that a certain delayed train will just be too disruptive to the network, so they're forced to just cancel a train to try and save the network's stability.