What doesn't sound right? You might be saying the same thing. To store this appointment correctly, you store the timezone of the appointment (let's say EST) and the timestamp within that timezone (4pm). So the final version is 16:00 EST. You can store a UTC version as well, but you need the local timestamp and timezone first.
If you only store the timezone with a UTC timestamp, when you convert back after DST shifts you'll end up with 3pm or 5pm (depending on the shift), not the expected 4pm for the actual meeting. UTC in this case is not the anchor, the local timestamp the user set for the meeting is.
