I'm curious to understand what process they are not following. Is it your policy that they must deposit all cash and withdraw funds to replenish the machine so that you can reconcile the withdrawals to the incoming ACH from the ATM processor?
We had several low/moderate volume ATM owners that replenished machines themselves. When reviewing them, I would look at the incoming ACH from the ATM processors over a period of time and add that amount onto the cash deposited during that same period. If I felt that the cash deposited plus the cash they put in the machine was excessive then I would investigate further, but if the total was within reason, I documented and moved on.
I agree that having only part of the relationship makes it much more risky since you are now in the dark about the ATM volume in relation to the cash they are depositing.
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