Ultimately, the issue before the SCOTUS is a semantic one about how to characterize Aereo's business: does the company stream content over the internet to customers or does it provide customers access to equipment that lets them stream content to themselves. While such a distinction may seem trivial, it's the difference between breaking copyright law and abiding by it.
Aereo argues that it's a rental service of sorts, giving folks access to the equipment needed to pull down over-the-air TV broadcasts and either stream them live or record them for later consumption over the internet. Such equipment can be bought and used to the same effect by any one of us for our own, 'private performances' without running afoul of copyright law. Accordingly, argues Aereo, because its tech merely enables each user to access his own antenna and own cloud DVR remotely, using that tech should be considered a 'private performance' under the law.
We now know that the DoJ believes that Aereo is re-transmitting broadcaster's content to the public -- not unlike a cable company -- and is therefore in violation of Federal copyright law. The government says that, while Aereo uses individual antennas to receive the signal, it pipes all those signals through centralized servers and other equipment to service its customers collectively. So it's not an individualized end-to-end system like the type individuals can legally set up and use. Furthermore, Uncle Sam says that when Congress passed the Copyright Act of 1976 (the primary law governing copyright), it did not equate individuals and commercial content providers. So, According to the DoJ, that means Aereo should, legally speaking, be treated like Netflix and Comcast: companies that re-transmit copyrighted works, and therefore have to pay to license them.
Oh, and the government also informed the Court that its position doesn't mean it's against streaming video, cloud storage or new broadcasting technology -- as long as the content being stored and streamed has been bought and paid for.
What's all this really mean? Well, nothing... yet. The brief is what amounts to a piece of advice; the Supremes are free to ignore it. But the DoJ's opinion carries governmental weight, and could certainly influence the Court's ultimate decision. We'll just have to wait until April 22nd, when oral arguments are held, to find out just how much juice the DoJ has in the highest court in all the land.