Trout-
My understanding is that the bank that holds your account imposes a max withdrawal every 24 hour period. For example, I've taken 1k out of a machine and I know that that limit was imposed by my bank not the bank that owned/operated the atm machine.
With that said, I was in San Fran once and needed cash from an ATM that was in a convenience store and the most that it allowed me to take was $250 even though the max imposed by my bank was higher.