I don't understand how they can issue a ticket to the owner without proving they were driving
Nobody's considered guilty, it's an administrative ticket.
No points are removed from the owner's driver licence because they can't prove who was driving but the owner still has to pay the ticket.
The gist is that it shifts the burden to the accused to prove they were not the driver at the time, whereas when you are pulled over, the police are verifying it right there.