(I am running Windows 7.)
Yesterday I did some clean-up and moved some mp4 files from my desktop to "My Videos". Later I got a message that my OneDrive was almost full. Then I realized that when I had put the videos into "My Videos", they magically got put into OneDrive as well. Deleting them from OneDrive deleted them from "My Videos" as well. Restoring them in the Recycle Bin put them back into both places.
Right-clicking OneDrive, it appeared that this shouldn't have happened, since
under Settings, "Let me use OneDrive to fetch any of my files on this PC" was not checked;
under Auto Save, "Automatically save photos and videos to OneDrive whenever I connect a camera, phone, or other devices to my PC" was not checked either.
(My answer appears below -- if someone has an alternative answer I'm all ears.)