There are several types of verifications when it comes to crypto ATMs, and again they depend on the individual country and its legislation. What you describe is withdrawing money into your bank account, but most crypto ATMs are only one-way devices, which means you can only buy crypto with cash.
Some of them will only ask you your mobile phone number on which you will get confirmation code, others will ask you to show your ID on the ATM camera, or to show your face in front of the camera. Some ATM are using special software (check
https://shuftipro.com/).
I think the USA has fairly strict laws in this regard (FinCEN) which requires that all clients in such transactions are identified, all of course for the purpose of preventing money laundering and terrorist financing.
Maybe Finland is one of the first EU countries that is starting to implement new EU directives (AMLD 5) which came into force on January 10 this year.
KYC is as diverse as the many countries where there are Bitcoin ATMs. This means that for now there is no universally accepted KYC procedures and this all add more inconvenience and confusion to Bitcoin holders, putting more reason why up to now Bitcoin has not yet achieved the massive use it should be enjoying. Here in my country, I think we only have two or three existing ATM terminals where one can be able to transact Bitcoin but KYC is not yet that very strict but we know that soon this can be changing. Let's hope that there can be a common procedures for this one so that Bitcoin users will not be left on the cold as far as ATM is concerned.