Well, why don`t you really give the money back? I suppose there has been a mistake and paypal has added more money to your account , which actually do not belong to you.... I believe it is not worth trying to prove this money belong to you , when they don`t ... right?
Cheaters like to make business very hard.. Do you even need to ask if you have to pay? If you don't pay they will whatever they could to collect their money..
I didn't realize it's possible to make negative balance. Yes, you should contact PayPal and pay this debt, unless you want to spend some time in jail for doing fraud.
As you have got the product they can track you easily at your address and you are from US so you may have tough time, better you call them and solve the matter at the earliest
No matter how, you purchase the goods and surely you need to pay for it. Else, you can be sued as stealing. I think it is not worth to go into the jail for $1269
Read your user agreement. It says if you don't pay it they'll send it to debt collectors. Not sure about jail time. Has it been a year? If so, then unlikely.