Have things changed on PP? When I had to verify my account, all I had to do was link a bank account to it and then go back to PP and enter the amount of the two small deposits they made. I never entered a SS# or provided other personal information other than my shipping address.
I can understand not wanting to provide personal information online. But being unverified will limit you as to the amount that you can spend/send via PP. I believe it's a "per month" limit and it's pretty low if you plan to do GC churning, even if you're paying with eBay GCs.