To add to the problem, social security was never meant to be an national ID number. It was just really useful for a whole lot of things. However, numbers are handed out sequentially, not randomly. So take your SIN and add or subtract one from it and that is another person’s SIN. Knowing just a few simple things about a person can reveal most if not their entire SIN.
Party lines! You’d share your phone line with one or more other households. When the phone rang they all rang with alternating short-long rings to identify which house on the line the caller intended to call. So if someone calls you at 2am, several of your neighbors know about it because their phones rang too. Even better, being a snot nosed kid I knew how to take a set of headphones and clip them onto the line. You’d hear both sides of the conversation of any house on the party line without dropping the call voltage too much and getting caught. That meant no one talked about anything private on the phone, everyone else could be listening.