I believe the video is somewhat incorrect: Arc (and Rc) need a reference count, which you missed in your description of the overhead. (EDIT: You mentioned this later in the video. )
The downside of all of Arc or Rc is of course (as you pointed out towards the end of the video) that you need to do all that reference counting and store the reference count (as I mentioned above). A box of a slice would indeed be cheaper. But if the data is static (or will at least live for the rest of the program), you might consider just leaking it (Box::leak) to get a static lifetime reference. That can then be cheaply shared.