Dear Avira,
This is the sugya. The Chassam Sofer used the Rashi from cheese for milk. The Chazon Ish is completely rejecting the comparison. Same as Rav Moshe. If you go through the nuance, he is even more lenient in theory. There wasn’t a reason for the Chazon Ish to pasken. He was never in a country that had applicable standards for the milking process. And the heter of the government had already been in use for decades. The heterim of the Pri Chodosh had already been relied upon in parts of Europe.