2. I don't even understand how a title transfer could happen without verifying ownership. Is the title system in the USA decentralized or that much different than elsewhere? i.e. Torrens-style
It wasn't easy to clear up, either. I'm fortunate that a close friend worked (at the time) for the SS administration, and was able to do basically all of the leg-work for me: I just had to sign a few forms he sent me. Someone not equally connected would have had a much harder time.
I'm also painfully aware that effectively every scrap of everyone's personal data has been repeatedly leaked online. I doubt that any amount of care has much to do with whether or not I'll be targeted at some point in the future.
This person could have been an illegal, but there is a non-zero chance you just both had the same one. It does happen, or at least did.
Sidenote: I don't bear any ill will towards whoever used my SSN. It's not like I was targeted, or even that any harm to me was intended. This was a "hack" of a dysfunctional immigration and employment system, in a way that's totally obvious and easy to anticipate. My ire is reserved for those in positions of responsibility who maintain a regime that is manifestly not fit for purpose.