Mystery solved. It ended up being that a designer had put an !important on display block for the links, therefore overriding the ‘none’ that was in place.
Just realized you can call the calendar page with ids specified, and have the calendar categories limited that way. I think I can use that as a work around.
For instance:
calendar?ai1ec_cat_ids=365,367
Thanks again for all the feedback.
Thanks for the quick feedback guys! In regards to the suggestion by smithgt, I assume this only works with the widget? Nothing to allow the full calendar on the page?