I have been receiving Avdata every month for the last eleven years, so have some experience with the system.
They do determine billing based on radio data, and yes, they often do make mistakes. However, they have always corrected my bill when they they have made mistakes.
It has been irritating to follow up the mistakes but they are pleasant to deal with and I have never found them unreasonable.
Avdata provides a very convenient way to collect landing fees for aerodrome owners, so that is why it is so widely used.
They only charge for landings, including touch and go's. In the Skippydiesel's case Avdata has made a mistake and they have corrected it.