Aereo did the TV version of this, renting each user an antenna instead of renting DVDs. Its outcome may be instructive.

https://en.wikipedia.org/wiki/Aereo: …the U.S. Supreme Court ruled that Aereo's services breached copyright laws. It ruled that, "viewed in terms of Congress’ regulatory objectives, these behind-the-scenes technological differences do not distinguish Aereo’s system from cable systems, which do perform publicly", and that "insofar as there are differences, those differences concern not the nature of the service that Aereo provides so much as the technological manner in which it provides the service."