Shows do often start a minute after the hour or half hour. It’s actually something that the networks do to keep you from switching to another channel. The time displayed should be correct as the data comes directly from the local broadcasters.
This article explaining the why is from Australia, but broadcasters in the US & Canada do it too:
If you’re looking for someone to blame, it’s Ted Turner:
Other networks looked at what he was doing, and borrowed it for some of their programming.
As for late-night shows, you can apparently blame Desert Storm:
We were trying to limit the number of options available in order to keep things simple. We felt that the 2 minute option would cover the most use cases.