It was OOP that chose to escalate this to malicious compliance and ascribed a lot more to her attitude than what's actually said. OOP assumed that she was out to get him in specific, when nothing in the described call even suggests as much.
The correct response would've been to ask for the manager and if the manager chooses to stonewall in an obnoxious way (which is possible!), then you pull the frustrating fax from hell on them. At that point, you're not just speaking to someone who has no power to fix shit, you're talking to someone who does have the power to fix shit and chooses to be a stick in the mud about it. That's when being a jerk back is deserved.
Being a jerk to low paid employees in this manner is unacceptable, rude and makes me think a lot less of the person writing it.