There are apparently multiple cases of Hertz doing this, at least some of which apparently included the person having the physical documentation on their person at the time of the arrest, including the Steve Cheney incident and one in Louisiana.
.. do people NOT do this? Like, that paper agreement is the same thing as your title as far as having a right to operate the vehicle. Why would you NOT have your agreement? Insanity.
Print whatever they send. Print it: it is worth the effort: you will not convince the police with a phone but you might with a paper.
Digital is OK until you run out of battery or anyone refuses to accept your phone as proof.
When you hire a car you are just hiring a several-thousand-dollars item from a stranger. Either you take it seriously (and have a paper trail, hence) or you do not understand the risks.
I recently read of some hapless tourists who rented a car, parted it at a trailhead in the Santa Cruz mountains and when they got back from their hike it wouldn't start because it couldn't contact the mothership.
Seriously should be a felony to posses a device designed to remotely shut down an automobile.
Keep paper records with you at all times when renting something.