Anybody have any experience with this?
It depends. As I understand it, Paypal needs your SSN when you have reach a certain limit(make $20,000 a year)and this is a US federal law mandate. Are they asking for your whole SSN or just the last 4 digits? Anyways, this link has almost the exact issues you're worrying about:
https://answers.yahoo.com/question/index?qid=20120602143147AA2F98U
Anyways, if you do feel all this is shady, contact a Paypal representative and see if everything is in order.