Okay thanks for getting back to me @LeonidS! I figured out a workaround, and it's completely perfect, so I'll post it here in case someone finds my topic looking for a solution to a similar issue.

Basically, we wanted to create events (members-only guild meetings) that were automatically visible to anyone who was a member, and automatically can't be seen if someone isn't a member. But the events - including all of the old ones - needed to be browseable on the site, even if someone does not have a direct link. The easy way to accomplish this was by putting the events inside a Group.

How to create a browsable section of members-only events on an UNA site:

I created a Group "Guild Meetings" with visibility set to all membership levels except unauthenticated. Then the guild meeting events were created with visibility set to the group "Guild Meetings." Finally, I added a link to the group in the menu that shows up to the left on the home page:

That menu is at Navigation > System > Profile Stats. I used "Add new item" and pasted in the entire URL to the group, and UNA automatically converted it to the code line.

We use the group description and info for "Guild Meetings" to explain to members how guild meetings work and how to attend, and we tell them to click the "Events" tab to browse all past Guild Meetings and view recordings.

All the default UNA settings work perfectly for it - there is a calendar widget on the Events tab where people can look up a meeting by the date it happened. If someone is logged into their account and clicks a link to a meeting, they see the meeting info (or embedded video recording if it's a past meeting). If they're not logged in, they see "Access Denied".