> This was tried before with the "rent a DVD and player" streaming service (Zediva).
A huge difference between Zediva and Aereo is that Aereo only rebroadcasts network television. All the content that Aereo rebroadcasts is already required by law to be publicly accessible and unencrypted(!)[0]. This is why they only serve over-the-air content - the same law does not apply to DVDs rented, or even to cable television.
Also, to my knowledge, Aereo does not deduplicate content stored, whereas Zediva essentially does. You and I know that there's no difference between "my" digital copy and "your" digital copy, but Aereo does store a separate copy per-user and only distributes each copy to the correct user.
The reason that Aereo separates those copies is because we already have case law that establishes my right to record an over-the-air broadcast and replay it for myself[1]. Aereo maintains that it is acting on behalf of the customers to exercise the customers' right to create personal recordings. If they de-duplicated the data (as Zediva did), they'd certainly save a lot on storage and hardware costs, but they'd no longer be protected by this legal precedent.
Aereo has a very well-funded legal team that is certainly aware of Zediva and other landmark legal precedents[2] - they specifically crafted their entire business around the Cablevision ruling and other case law.
[0] In 2012, the FCC decided to allow cable operators to encrypt these signals, but even this only applies to the retransmission: "The FCC wants to ensure that consumers can still access basic cable services without specifically renting a box from the cable companies. And so the FCC is requiring that the cable operators make the unencrypted TV signals available to third-party device makers and Internet TV service providers." (http://www.cnet.com/news/fcc-allows-cable-operators-to-encry...)
[1] https://en.wikipedia.org/wiki/Sony_Corp._of_America_v._Unive....
[2] Aereo's raised $100MM in 4 rounds. Three of those rounds included IAC, which is run by Barry Diller, who has plenty of relevant industry experience, to say the least: https://en.wikipedia.org/wiki/Barry_Diller