You more or less have to have some bank account that's directly linked to your PayPal account and set as the default, and then you can choose a backup source of funding if that bank account doesn't have enough funds for your purchase. I have existing accounts with ING/Capital One 360 and they make it pretty easy to open multiple accounts so that you can do things like have targeted savings accounts that don't have fees. So, I opened a new savings account and transferred just $1 into it. I confirmed with the bank that overdrawing on a savings account wouldn't cause a fee from them:

So, my thought is that if I accidentally didn't change the payment method when paying for a purchase with PayPal, it will always go over to the backup funding source since the linked bank account only has a $1 in it.
DISCLAIMER: I HAVE NOT ACTUALLY TESTED THIS YET, YOUR MILEAGE MAY VARY! (aka I can't guarantee that this actually works, but I'll update this post if I ever end up testing it and can confirm its effectiveness one way or the other.)