If the customer was only renting space for the ATM and the tenant was servicing it, the contract would suffice. Since the customer is servicing the ATM, the expectation is that you will monitor the activity. If the account is not at your bank it's unlikely you will meet that expectation.
As for requiring the customer to maintain an account, banks hold the carrot as well as the stick. You can give them a free, ATM dedicated account (much easier to review) or, if they don't like it, charge them a fee for reviewing the ATM activity going through their general account.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.