The airport information desk at my local (regional) airport gets its estimated times from the ground handling companies and not ATC. The handlers are copied in on all relevant movement messages from the departure airports and the information desk is subsequently updated as necessary.
However, messages may contain estimated departure times as the aircraft is expected to depart late, and therefore any time passed to the information desk is purely provisional. Even when the aircraft has actually departed, times may contain 2 errors.
Firstly, many ground handlers fiddle departure times to try to maintain an illusion of on-time performance when in reality the aircraft departed late (if all aircraft are ever fited with ACARS this might no longer be a problem, but you'll see O'Leary join the clergy before that happens). Obviously arrival times at the destination will reflect this innacuracy, with the aircraft arriving later than estimated.
Secondly, the arrival time is also based on the aircraft flight time. Again, not all ground handling agencies provide an accurate flight time, or use flight times based upon older and less capable aircraft (easyjet for example still has flight times for many routes based upon the 300 series 737 and not the more capable 700 and aircraft routinely arrive well ahead of schedule). If flight times are little more than guesswork, then clearly arrival times are going to be a work of fiction too.
I can assure you that it is not just the public that find this frustrating. It plays havoc with operational planning too.