From the user's perspective it is the same appointment. They think they have an appointment at 3:00 PM on Thursday. If there's a timezone change, and you just stored an integer, then from the user's perspective the meeting changed from 3:00 PM to 2:00 PM.

Of course, if you have a meeting that spans timezones, this is unavoidable. I think the real solution actually lies in how the meeting time is expressed to the user so they don't have misconceptions about it.