There is no way in hell they cannot know what they are doing. They know they're not from Microsoft. And given this scam has been in the news for a while now, they don't get to plead ignorance.
I agree that they know its a scam, I disagree that they know who their employer is.
I have seen interviews with some of the rank and file scammers. Apparently, they do it because the pay is good for someone with their skillset and ability to put ethics aside.
The people who are on the phone don't know the details of the corporate structure. The boss could easily lie and claim to be a Microsoft contractor and it might be hard for someone on the phones to verify and asking to many questions might get them fired. This might make it easier for some to set aside those ethics, they know they are not on the level, but can feel slightly better because they think their behavior is authorized by a large company that already services these customers.