I suddenly remembered that long ago, for whatever reason, I had made two other Photobucket accounts (one in 2004 and one in 2005, according to the registration dating; they looked to be empty, so I had deleted stuff years ago in there). I vaguely remembered the ancient e-mail addresses for them, but not the usernames. Using the former, I was able to get the latter. So now, they are deleted, too.
And with that, I have cut ties with Photobucket completely.