I'm not sure about legal liability, but having your name on the machine is going to create expectations for those who use it.
As you indicated, if the machine fails to dispense, or someone disputes the amount, timing, or existence of a deposit at that machine, they'll come to you expecting you to have full access to it to settle the issue. If the service company charges you for this, that may begin to add up fast.
Likewise, if your state passes any specific laws concering ATMs (i.e. the panic button laws) may result in your bank being involved in any litigation involving it. Also, any law enforcement that wishes access to ATM footage may come to your bank rather than the vendor.
I can see this causing you a lot of headaches if you don't own the machine. On the bright side, lack of ATM fees is a good sales/customer service point. Of course, if they can offer that option without the name, then it might be worth looking into.
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The above is my opinion, and is frequently valued at USD 2ยข or less.