Firstly, let me re-state that I think that the law itself is wrong and unjust. But that's different from saying the Supreme Court interpreted the law incorrectly. I don't see why it should matter how a customer receives a broadcast within the service area of that broadcaster. However, given that legislation for this sort of situation exists, I think the Supreme Court reasonably interpreted the law.
Aereo thought that their setup with individual antennas was a workaround for retransmission fees. Turns out it's not. When the law has any ambiguity, the courts (and certainly the Supreme Court) gets to decide what the law is. Which means their legal interpretation may have been plausible (I think it wasn't) but the losing side in a Supreme Court case is, by definition, in the wrong (until the law changes, anyway.) That means cable providers can't avoid fees the way Aereo did; because Aereo was blowing smoke.
The law (written in the 70's by Congress) said that taking the signal and retransmitting it was a "performance" requiring the licensing of the content. It originally was written in response to "community antennas" that filled in gaps in broadcast reception, but over the years, it also applied to Cable TV systems, satellite providers, and IP-TV providers like VIOS and U-Verse. The court decided that capturing the signal remotely and packaging it up over the internet qualifies as a retransmission, no matter how many antennas you use. This is not an unreasonable decision here. Frankly, I'm not sure why Aereo thought that an array of tiny antennas was a "magic wand" to let them avoid fees that a provider like VIOS or U-Verse, (which produce the same end-result (an individual video stream of a broadcast over the internet)) must pay. Courts generally don't like the "magic wand" way of resolving legal responsibilities; they frown on cumbersome things that make no sense outside circumvention of a legal requirement. (In a similar vein, a tax shelter must have a genuine economic purpose to be ruled valid; otherwise it's tax evasion. And it's still money-laundering if a bank sees a depositor split up payments to each be $1 below reporting thresholds.)
(As a side-note, that law in the 70's was written in response to a specific court case where the court said re-transmission wasn't a "performance" under copyright law. So Aereo would have been correct prior to that law being written, but they were bitten by the clear intent of the law.)
This decision reminds me of the shop a few years ago that thought they could set up a Video-on-Demand service by plugging up an array of physical DVD drives in their data center, thinking they could get around continual performance royalties through the one-time purchase of a DVD. They lost too. Again, the court frowned on a cumbersome setup that made utterly no technical sense put in place just to try and avoid the law.
And the court was careful to narrowly scope the decision to prevent it from being used to stop people from doing things like backing up their music collection to Dropbox.
Ranting about bought and paid-for law isn't really relevant here. Since they are Supreme Court justices, they can utterly ignore political and corporate pressure and rule any way they damn well please. That doesn't mean justices are always right, but criticisms that might normally apply to Congress and elected justices aren't really relevant to judges with lifetime appointments.