It happens when you add DNA test information. The difference here is that William added a test for someone who is not a member, which is fine as long as William is the manager of the test information.
A "side effect" of this is that adding DNA test information adds a badge to the profile. The badge isn't visible on a non-member profile, and so to William it looked like he hadn't added anything. (And the same for you if you've added tests for non-member relatives.)
By the way, William, I was in "sysop land" while I was talking about that. What I should have pointed out is that if you want to add/change information about the test you added, you can go to the profile menu and click on the DNA link and then DNA tests. There will be a button on that page to edit the information you entered previously.
Again, hope that helps, and I apologize for any confusion. I hamstrung myself today by trying to do too many things at once. :-/