After a post here mentioned it, I went to WP:COI and WP:AUTO.
These two articles seem to promote the view that you're not supposed to edit an article about yourself.
However, WP:BLP seems to suggest that you can to remove libel or unsourced material, and it's a common refrain to complaints about Wikipedia, "why didn't you just fix the article yourself?"
It just isn't consistent to both expect people to fix the article about themselves, and expect them not to, at the same time. It's true, of course, that neither WP:AUTO nor WP:COI are absolute prohibitions, but they discourage it in *such* strong terms that anyone who comes to Wikipedia with a complaint about an article about themselves and stumbles across either guideline, will think that fixing the article isn't allowed. The subtlety that "strongly discouraged" doesn't mean "prohibited", or that even a new user is permitted to violate a guideline, is something they'll completely miss.
How can this be fixed? I complained on the COI talk page and nobody seems to care. And I suspect just editing the guidelines myself would be reverted within the hour.