Everybody should read this .pdf file. They say in plain language that they collect SSN, not last 4 of SSN (page 2). It also say what else they collect which I've already included at the top of the list. As far as I know most Bluecheck vendors are only asking for last 4 of SSN.
What good is the last 4 of the SSN if they don't have the whole SSN? Can any of these AV services get our whole SSN?
The last 4 numbers are frequently used as a cross check for identity. It's just one more data point to see if you have the right John Doe born 1/1/1960. People move, people change phone numbers, people don't change the last 4 numbers of their SSN. Even Veratad will collect it in certain situations, although it sounds like they don't necessarily keep it on file with your other information.
They should not retrieve your full SSN unless you give them permission, for example in a credit application.