You're both correct.

The scheduling library should be more upfront about /what/ is being agreed to and force the user to pick.

P) The event is at a precise internationally recognized moment (better for co-ordination globally).

R) The event is in local time (like a lunch date) and expected to remain colloquially fixed.

In the case of the first you store a precise UTC timestamp and drop the timezone (it's UTC).

In the case of the second you store /how/ to pick a UTC timestamp based on a time in a timezone.