Ah, my mistake – they’re all pingback emails. I hadn’t looked carefully enough at the emails. I just registered the ‘please moderate’ emails after doing an update. But should there be a pingback request from the site itself? Isn’t WP clever enough to know the links are from the same site? I don’t think this has ever happened on my WP installations.
I will just disable pingback notifications.
Thanks for replying and making me look more carefully at what was happening!