Earlier quoted context omitted.
Wonderful summary, and I agree with your conclusion: people should take this as the Court saying "no" to Aereo's contrived, free-riding business model, and others like it, not to new technologies that enable people to store and access content which they already own [a license to].
Can I set up my own antenna in New York and stream its recordings back to myself in Minneapolis? How long is my antenna allowed to be before it magically switches to becoming illegal? This is an incredibly stupid decision that raises many more questions than it answers.
The entire reason this law was written is because under an old law, cable companies ("community antenna television" in that day) were setting up antennas and running cable to multiple homes, charging the users for it, and not paying anything to the broadcasters/copyright holders. They made the same claim Aereo is making now - we're not rebroadcasting, we're just a big antenna connected to multiple homes. The law was written specifically to address this, but it was written in a generic way to avoid loopholes... like exactly the loophole Aereo claimed existed.
The gist of the supreme court decision is that, despite the behind the scenes trickery, Aereo is essentially no different from a cable company as far as that law was written. The intent of the law was certainly to restrict companies exactly like Aereo, and the letter of the law gives the court the ability to enforce this intent.
Before you call the decision "incredibly stupid" you might want to actually read it.