“He also used the hum’s continuity to show that [the recording made by the police] was indeed a single, undoctored clip”

The police are the ones who are making use of electrical hum. That means they have the necessary records to fake electrical hum.

All you'd need to do to take hum is filter out the 60Hz/50Hz hum with a notch filter, and add back hum recorded from the location of your choice. In fact, it'd be good to develop some tools to do just that to ensure its not just the police who have the ability to fake it.