Never thought about Bitcoin ATM as a anonymous way to buy. I'm guessing there's plenty of surveillance that can tie you to a purchase, and not sure what records are kept on the Bitcoin ATM itself in terms of timestamps and transfers. Probably better to use local ones ;)
Which leads me to wonder why Bitcoin ATMs are valuable at all given that the fees are higher. Hum....
I've not tried using a Bitcoin ATM (though there are a few here in town. If you buy with cash there shouldn't be any records to keep other than transaction and wallet info. Of course if an address is known to be your address, then I guess the anonymity is gone.
Better to just use Monero ;-)