Buying thru Bitcoin ATM is number 4 on the list, I guess it depends on the jurisdiction, USA might be requiring ID to use the ATM, because as mentioned in the article it only requires you to scan your address or if you don't have an adress the ATM will generate paper wallet for you.
Try to find other bitcoin ATM since there are a lot of them in USA. Good luck, hope this helps.
I doubt op can find an ATM in US where he can purchase BTC anonymously due to the regulations imposed by the government. If he wants full anonymity, he needs to stick to sites like LocalBitcoins, Binance etc in this aspect.