Paying good money for free television

Completely amusing:
At my house, we recently upgraded to the Netflix plan that involves both DVDs and unlimited streaming. We also picked up a new DVD player (Blu-Ray, bluray, Boo Boo Ray, what is this I don’t even) with built in wireless Internets, too, so we can hook up the machines to the Netflix and watch the shows on the old 4:3 TV in the living room.
OK, that’s not the amusing part; this is:
We’re doing this to watch Downton Abbey (grown ups) and Sesame Street (kids, mostly).
Honest question: Do PBS and related organizations get a cut of what we’re paying Netflix?