Andrew and I did a little more debugging on this and found that anything in the browser that supports drag and drop causes the calendar drag and drop stuff to turn on.

This means any links (which are draggable by default in browsers) cause the calendar drag and drop to become visible (though it doesn't work if you try to drop something there).

It also explains why dragging and dropping of action events appeared to work despite them not being draggable. It's because they have a link in them and links are draggable by default.

The calendar drag and drop code needs to be changed so that it only responds to draggable="true" calendar events being dragged.