Ok, so… the issue is how the #top-section title is being called. The titles within The Events Calendar page templates themselves were calling just fine, though. I’m not sure where to go to find the code for the top section, so I just “hid” those titles via custom css:
.single-post #top-section header h1, .events-list #top-section header h1, .events-archive #top-section header h1, .tribe-events-page-template #top-section header h1 {position: absolute !important; top: -9999px !important; left: -9999px !important;}
It’s not something I could test in a base theme like Twenty Twelve because this is a special header title separate from post titles and Twenty Twelve, et al don’t have that particular feature.
Anyway, if anyone else has a similar issue – sorry I don’t have a decent solution, but… there ya go. You can at least hide the offending sections for now. If anyone else encounters the same problem and finds a php solution, feel free to post it here. ??