This has nothing to do with the couple prerequisite related parameters in configuration. This message is showing because you have a prerequisite event and/or prereq category selected in your event. There is NO other reason why it would show. Sometimes people select the event's category in the prerequisite category area without paying attention to what it is. This is probably what you did. Use CTRL-click (or Command-click on a Mac) to de-select any category or event that you selected in the prerequisites area.
Funny, no prerequisite events or categories have been selected, and whether I am logged in or not logged in, same message for both events that I've published...
The message clearly states: Before you can register for this event, you must have already registered for the following event(s): (I would imagine that it would show a prerequisite event in this spot if it had been configured to do so)
I promise you a prerequisite category is selected. By default, the prereq message doesn't include the tag for categories. There is no way this message would ever show unless you have a prerequisite category selected in the event. De-select it in the event setup.