I'd like a non user to be able to enter the time and date they would like to be reminded about an event in the public access.
The other option would be this:
If a user subscribes to the calendar, they get the can add their own events. What if there were a way to have the public access calendar automatically embedded within each new calendar registration. Of course, they wouldn't be able to alter public events, but they could in fact set reminders for themselves.