I have a subsite which has modified permissions. It does inherit permissions from the parent site, but I also added a new group with read-only permissions. By giving the group read on the site, they automatically got read permission to all pages and documents, exactly as expected. There is also an Asset Library added to the subsite, but for some reason this is inheriting permissions from the parent site, not the subsite, which meant a lot of error reports when users couldn't play the video files stored there.
I confirmed this by opening the Advanced Permissions page for the Asset Library, then clicking Manage Parent--I got the main site's permissions, not the subsite's. On the other hand, the Asset Library appears in the subsite's Site Contents, not the parent's.
May I assume this is a bug in SharePoint Online? Any ideas on how to connect the Library differently without changing every video URL I've already used on various pages?