The other responder suggested that the coordination is handled differently.

If you know the periodicity of a signal you can violate the Shannon Coding Limit. It's just that most signals you have to have a high enough sampling rate to detect the period, which gets you back to Shannon.

The LHC signal has out of band data that you can use to establish exactly when to take a sample, and the samples happen exactly 40 million times per second. So once you tune the time offset, the period is precise.