I just edited the link in Jon Skeet Facts and I got an Organizer badge for it. I didn't retag anything, though. Bug?
This was a bug around awarding the badge and deletion, it will be fixed in an upcoming overhaul of the badge code next week.
I think this is related to the fact that when you reach 2000 rep (or 100 for CW on meta), there is no re-tag per se, only edit, which may count as a re-tag from the perspective of the code.
ie: I don't think the code checks what you edited (body, title, or tags) when you edit a post
I just had the same thing happen. I edited some grammar in this SO question, which was re-tagged by the edit previous to mine (which occurred some 14 months earlier). I did not change any tags, but was awarded the "Organizer" badge. I also had over 2k rep at the time.
It seems like it only checked that I edited the question and that the question was re-tagged. I wonder if someone can test to see if you can earn other, potentially similar badges like "Cleanup" in this manner.