I think one major point you're neglecting is that the customers are paying the ISP (Verizon, in this case) for Internet access. Netflix, YouTube, etc., are all paying their Internet providers for Internet access. Nobody is getting anything for free.
Here's an example to contradict your truck example. You have a private mailbox at a store that doesn't care what package carrier you use. That mailbox costs you a monthly sum to maintain, and in return you get an address, someone to receive your packages, etc.
Now I want to ship a package to you. I choose UPS and pay them to have the package delivered to your mailbox. Once the package reaches the store, the owner of said store decides that, even though you've paid for your mailbox, they're not going to deliver the package to you unless I (the sender) pay them directly. Nevermind that you've already paid for the mailbox, and I've paid for the cost of transporting the package to their door, they feel they deserve additional money from me to give you the package, even though the only reason you have the mailbox in the first place is to receive mail.
That is exactly what Verizon is trying to do.