I think most rail systems do this; it would be considered a reliability problem, not a punctuality problem.
You definitely have to be careful with the definition of these things, though. For instance, Irish Rail considers intercity rail to be on time if it's within 10 mins of schedule. Commuter is within five minutes of schedule. Given that, at peak times, some commuter services run once every ten minutes, and thus are ~always on time per this definition, it's wise to be a bit skeptical of the punctuality reporting.
I think that makes sense. If a commuter train leaves every 10 minutes, but due to some technical problems, the first train of the early morning leaves 20 minutes late which then continues through the day, does that mean every train is late? The users wouldn't know the trains they're using should have actually ran 20 minutes ago, they just know a train is to go every 10 minutes.
I think the Swiss actually do something like this, whereas in Germany they've only comparatively recently started doing it, too, and even then I think they're currently only looking at long distance trains, so connections to/from regional trains don't count (and never mind local public transport).
If you set out on a high-speed train journey, but your train stops at a station halfway to your destination, waits for an hour due to technical problems and then is canceled, that's a delay from the rider's perspective. However, when the Deutsche Bahn publishes its official on-time statistics, this train will not be counted as late.
In its public messaging, the Deutsche Bahn emphasizes its on-time rate. "We have an on-time rate of 65%" sounds like "You'll arrive on-time 65% of the time." If you're actually sitting in the middle of nowhere, with the next train an hour away, that doesn't feel like being "on time."