Take your social security number. Change the last number by one. Congrats, you have stolen someones number.
It isn't secure or random in any way. Infact, by doing the above you will have the number of a person born probably in the same hospital as you.
The address does make it a lot more useful, but the point that I am making is simply that the number itself has never been secure, and this kinda failure was inevitable due to only needing slightly more info than the number itself. A number which itself is already partially identifying.
We shouldn't use social security numbers like we do.