Uhhh, that they don't have a PayPal account and they want to sign up?
You wouldn't be 'paying a third party' for it any more than depositing cash into my bank account would be paying Chase.
While PayPal isn't a bank, it's extremely comparable. Heck, I process credit cards through PayPal without ever sending the customer to PayPal (they would be none-the-wiser that we were using PayPal as our Credit Card gateway) so the desire to not 'pay via a third party web site' that is reputable such as PayPal is a bit silly, imho.
I suppose I have a different outlook on it, processing thousands of PayPal transactions per day.
Its funny you guys have had such bad luck because when i got mine hacked, they applied a provisional credit that was in my bank account in 3 business days. Ive never had an issue with them, aside from the language barier. But i deal with that at work every day anyway so im used to it.