I would never, ever drive off with a rental car without a hard-copy version of the rental agreement in my possession. When an Enterprise location some years ago e-mailed the rental agreement to me, I still insisted that they print a copy out for me before I left the counter.

Wholly apart from the possible complications if stopped by a cop, I always want to see the odometer reading and fuel level which appear on the agreement, so that I can compare them to what I actually see on the dashboard.