When I'm logging into my Apple ID (https://appleid.apple.com/account/home) in the tab "Password and Security" there are security questions, just like this article says: http://support.apple.com/ru-ru/HT201485
The thing is – I know answers to my security questions, I keep them in text file, just like my other accounts, so I have no chance to forget them. But nevertheless my answers are not right according to what the page says when I click "Continue".
Ok, I thought, then I'll try to reset my security questions. I read the article that I mentioned before (HT201485), but the thing is – there is no link to "Send reset security info email to [rescue email address]". And I do have 2 additional e-mail addresses.
I also checked the source code of the page. And guess what I've found:
"TODO add ability to reset CRs via rescue email"? That's above good and evil.
I know, that's very likely a duplicate, but I have some information that might help others with simular situation (in the my own answer below) and also I have a question:
How is it possible that my 100% correct answers suddenly became incorrect?
Best Answer
And that's the solution to my case.
I called to Apple Support and they said, that none of my additional e-mails was "rescue". I remember perfectly that in the time I registered my Apple ID there was no such option - just ability to set additional e-mail.
So, support reseted my security questions and now I can set a new ones, along with setting the rescue e-mail.