The different cards (and their underlying banks) use varying systems. The law says they have to verify identifying information, but does not specify to what extent. So some online applications are rigorous, others not so much---some check the SSN provided with government software that confirms that the SSA issued the number, and that it's still active (the person assigned it is not deceased).
Other systems check the SSN against the name, DOB, or address provided, to see if they match. And other applications don't do either, and just seem to check if the SSN is 'plausible' enough to be considered valid. Several "instant approval" reloadable debit cards (like Ready Debit) fall into this category at this time. The downside is the numerous fees that come with most cards of this type, and that the verification system for new accounts may get upgraded suddenly. The upside is that they can be used to provide a functioning card and/or bank account to address verify a stealth PP.
So if you want to set-up a stealth US PP that can fully verified, and can be restored following a limitation, first get a VBA and SSN confirmed PP (see the vendor in BST, or the product on vccandbank), and add a street address to it you can receive USPS mail from (family, friend, or maildrop). Apply for a easy-approval debit card using that address and the name provided on the PP. Once you have the card and have activated it, you can add a real bank to the Paypal.
If PP limits the account, you can address verify it using the card, and verify location by receiving the letter with the pin number to the real address you added, along with providing the photoshopped ID/docs they request. This should be enough to restore the PP, though there are no guarantees. If they deny your appeal, you can keep contesting the matter, or just wait the 180 days to withdraw funds to the working bank/card account. Think of Paypal as a beast you have to plan the middle or end game for in advance, in order to manage/mitigate your risk.