> just a small handful of nodesBut Netflix is not "just a small number of nodes". They're basically their own CDN; they have servers all over the Internet, precisely in order to not have the problem you describe.
What's more, Comcast has a deal with Netflix to directly connect Netflix nodes to Comcast's network; in other words, Comcast directly controls how many paths there are for Netflix content to get into its network. If there aren't enough such paths, they can just open up more.