When you install a server in a colo, you don't get free transit. You find a transit provider (like Level3, Cogent, or NTT) and you pay them for bandwidth. You can understand this very intuitively as most hosting services (like AWS) will charge you for bandwidth.

As a service provider (like Weebly), you are paying your own transit provider for a certain amount of bandwidth, and they are covering the costs of delivering that bandwidth to (usually) anybody globally and the costs of maintaining their network.

If a network gets large enough, they may often negotiate peering agreements with other networks. So Level3 and Cogent may have a peering agreement, or Level3 and Comcast may have a peering agreement. These are generally set up when two networks deliver roughly the same amount of traffic to each other, or it's considered beneficial to both parties to get the networks closer, and it simplifies the working relationship.

These peering agreements can often become contentious when they become imbalanced. Very early on, I remember a fight Cogent and France Telecom had over peering -- FT felt like they were getting the raw end of the deal, and de-peered with Cogent. Cogent refused to pay another transit provider for access to FT's network and so traffic from the Cogent network to FT would drop. They resolved about a week later, with lots of unhappy customers caught in the middle.

As you can see, it's simply not the case that (a) service providers never pay for bandwidth because the end-user already pays for bandwidth and (b) peering / free transit is guaranteed.

Maybe I'm not understanding the nuances here, but it seems to me like Netflix is taking an ideological stance to hide behind the fact that they are trying to negotiate a better business agreement for themselves.