I agree. What I should have typed instead of "The school is not intentionally installing spyware." Is they probably did not intend to install the spyware on personal machines of students that logged in with their school Google account. Perhaps there is a management policy misconfigured or the student got confused and enrolled the device.

From my understanding if you setup a personal chromebook you can then login to Google Classroom via the Chrome browser and it should not enroll the chromebook in MDM. At least when I login to my chromebook it does not enroll my device.