After more research it looks like the default calendar module uses ical.js which parses the ical link, since apparently ical is not a simple apples to apples thing. This allows the calendar at the private link to be displayed. Now I don’t know if FullCalendar has a limitation if ical.js were Frankensteined to interact with it or not. It currently seems to fetch the calendar data via API key and calendar ID. I’ll continue trying things, I don’t really know what I’m doing but it feels like progress!