[3np]

This reasoning doesn't hold if we're still operating within the base assumptions of RSA (and if we're not, no private key is secure)

[jagged-chisel]

Let’s try it this way: what if two people, unlikely as it may be, generate the same key pair? Two people know the private key, and factoring is still hard.

[hgsgm]

"someone might guess a key by luck" has always been an accepted risk of RSA or any key-based encryption system. It's an "act of God".