Disclaimer: I am not actually a lawyer, though I have spent a considerable amount of my life reading up on IP issues in law.
It is a legal thing.
Sony v. Betamax only established the legality of time-shifting as an application of fair use in copyright. It did not establish the legality of place-shifting.
Remember, under modern copyright law, the thing that is under the jurisdiction of the law is the act of making a copy. Whoever owns the copyright on an artifact literally has a government-granted and government-enforced monopoly on making any copies of that artifact. (I use the word "artifact", because of the large number of things that copyright applies to, including music recordings, maps, fiction text, and video)
What this means is that it is illegal to abridge that monopoly by making a copy--without the legal permission of the person who owns the copyright. Each and every copy made needs to be cleared by the copyright owner (although it generally is clearance in large swath, like "you can print copies of the book"), by law.*
To stream a video to a device requires, by implementation, a copy of that video to be created, which puts it under the purview of copyright law. This is exacerbated by the fact that in order to stream video generally means keeping a local copy (for at least some time).
The question fundamentally thus becomes: is the copying that occurs to a computer device considered the same from a legal perspective as the copying that occurs to a cable box and then from there to a TV set. The broadcasters say no, the cable company says yes. Or at least, whether the fact that customers are already paying for the service grants them a fair use provision to place-shift the content.
My sense is that if this were to come to the Supreme Court in the same way that Sony v Betamax did, that the Court would rule similarly: namely, that place-shifting falls under the purview of fair use. But this is just my sense, and who knows what the Court would look like by the time this got there, if it did, and whether my sense is accurate at all.
* Footnote: there is a set of exceptions to this monopoly power, which is called "fair use". While not a definitive list, there is, legally-speaking, a bright-line test for determining if a certain instance of copying constitutes fair use. An example of this would be citing a passage while writing a review of a book. The
Wikipedia page describes this well.
