In your example the towing company partners with AAA (so AAA directs customers to them) and the towing company guarantees quick service.
Up to now on the net the idea has been that all packets are delivered by your ISP to you as quickly as possible. The new model will be about throttling/delaying packets from companies that don't pay up.
It's as if AAA partnered with the towing company to get normal service for their customers, and in return the towing company would agree to show up late for everyone else.
Note also that Google already pays for all it's bandwidth to the net. You also pay for your bandwidth. Verizon is just acting to extract an extra tariff. Google is partnering with them to keep potential startups (without money to pay for normal service) in the slow lane so that they are unable to ever compete with Google's services.
This is evil through-and-through.