Security questions aren't really that secure anyway. A "real" hacker could just pretend to be helping out a friend after a debilitating accident and ask for everything to be reset.
Exactly, or the "crying baby/stressed out parent" example that made the rounds a few years ago. Hackers don't need to monitor every public comment you make, just trick 1 minimum wage call center worker for 5 minutes.
The answer could be: "Don't allow answering anything but this exact sequence of words: " then followed by a string of words.
Perhaps we need a reset contact whom they can call to confirm with a real human.