"The casinos are happy with you just giving them the number."

No casino is happy with you giving just them the number.
Somewhere along the line you have signed a W9 and your SS number is verified on your players card. You may have signed the W9 when you signed up for your players card.

Next time you are where you have signed for a jackpot, ask the players club to pull up your account. I am betting there is either your SS card or a W9 scanned into it.