Actually you can challenge PayPal transaction to your checking account. They come in via ACH, and there are well defined rules which your bank will be happy to advise you of, but you have a limited time to challenge them.
The real hazard however is in paying for things out of PayPal balances, or leaving balances in a PayPal account.
The PayPal Guarantee and protection scheme has more holes in it than a screen door, and the FDIC pass through protection might get you 1 or 2 cents on the dollar. Think about it. Insurance is $100,000 per account that PayPal holds, and on any given day, between PayPal balance, and transactions, PayPal probably has its hands on $70 million or so. How far does even 10 accounts go toward covering $70,000,000? about 1.5 cents on the dollar........
The real problem is that PayPal payments out of a PayPal balance are really non recourse transactions, and my advice is avoid them like the plague. A PayPal electronic check, ACH transaction, or credit card transaction is subject to recourse via Federal Rules and regulations from your bank. PayPal is carefully designed to fit in the space between a Financial institution such as a bank, and financial services company such as a stock broker. As a result, they are not subject to Federal regulation, or oversight, both of which provide recourse.