We are a company doing a PayPal competitor, we let user send money
online just like PayPal.  We would like to be able to allow our users
to do 2 things:

1) Withdraw the cash in their account into this ATM/Debit card, so
that they can withdraw it from an ATM machine (this is not really like
paypal since the balance on the card does not reflect the money they
have in our system in real time, sort of a basic requirement)

[Really nice to have, same as PayPal]
2) Have the card and our payment service share the same balance, so
that when the user receives money through our service, it will be
reflected in the card immediately.

I am aware of this answer: http://answers.google.com/answers/threadview?id=126634
We different in that we are not looking for a co-branded credit card,
our users have no credit risks since they cannot withdraw more than
what they actually have.

I am looking for specific banks that can do this for us, I know the
process already.  It would be best if you have verified that they can
provide this for us already.  Let me know if you have more questions.