It would never happen with any reliabilty... One thing that is highly unreliable is a human, especially a "non techincal" one being asked to do something "technical".
A "How to..." would help but I bet there are so many variations it becomes unmanageable and thus defeats its own object.
Quite, the base program needs to be set and checked by someone who knows what they are doing, no one else should have access to it. The same goes with room stats, someone will think "oh it's a bit cold" wind the stat up and forget about it.
This would be my prefered option. But I can't think of anything suitable off the shelf. A simple "press for heat button" in each room that turns the heating on for that room/zone for Y period. Subsequent presses of the button have no effect until the heating has been off for X time.
Pretty easy to do with a PLC and a bit of simple programming. The number of required outputs might be tricky(*) but you could use more than one PLC. Some PLCs have interfaces that can talk to modems but I'm not sure if that would provide interactive access or just a means of downloading logs uploading a new program.
(*) 1 output for the boiler and then one more for each zone so your zone per floor zone system should be possible with a single PLC. Requireing 4 outputs (boiler and 3 zone valves) and 6 inputs (3 room stats, 3 push buttons) I think...
Look at the Mitsubishi Alpha or Alpha2 series: