I've got a slightly different tale regarding privacy & emails misspellings. I have an email account that is [email protected] and while my name isn't particularly common there are at least 7-8 different people across the world with my name who have on more than one occasion had emails sent to me by mistake (by the namesakes as well as by others). I've never used what was sent to me maliciously, but I have on occasion tried to track down my namesakes to let them know of the error. I've been successful a couple of times, and know a few things that might be a little sensitive. I've managed to find the 'correct' email addresses of a couple of my namesakes & will forward things on when I'm certain who it's supposed to go to. My email address has been the recovery email for power bills, employers, dating sites, and a few other sites. Now imagine what could happen if I weren't the stand-up citizen that I am.
Godel's incompleteness theorem is actually even more subtle and mind-blowing than how you describe it. It states that in any mathematical system, there are truths in that system that cannot be proven using just the mathematical rules of that system. It requires adding additional rules to that system to prove those truths. And when you do that, there are new things that are true that cannot be proven using the expanded rules of that mathematical system.
"It's true, we just can't prove it'.