US credit card purchases are covered by the Fair Credit Billing Act, which gives you specific rights and remedies in case of problems with an order. The card issuer is required to comply with the FCBA investigation procedures.
PayPal as a whole is under no such constraints, and my experience is that they're just not interested in becoming involved in disputes between customers and vendors. (What if you fund the PayPal purchase with a credit card? It's a gray area...) Good luck even getting in touch with a real person at PayPal.
In response to the OP, ordering over the phone just gives them the opportunity to screw up your name, address, billing information, and order. The information is just going into their computer system anyway, so you might as well put it in yourself.