If I attached a digital broadcast antennae to my TV, wouldn't it appear to me just as if I were watching cable? I turn on the TV, I select among channels, I watch stuff. Or I attache the local antennae to a local DVR and use that. Same experience as if I had cable going to my DVR.
Yet despite the same end result I'm not watching cable.
Am I missing something? Is the experience not the same?
For better or worse, though, we've already decided we are going to look at more than just what the outcome is inside the home of the viewer, and consider at least some aspects of how the signal gets there. If you stick up an antenna at your location and receive a broadcast signal for viewing there (possibly delayed by a home recorder), that requires no permission. If you want to take those signals and stick them on a cable to distribute to your customers, or rebroadcast them through a satellite, we've decided that does require permission.
I think when Kagan talks about the same outcome, she means Aereo and a cable company are both third parties that deliver content from the broadcasters to you over a wire for pay.
Kagan is suggesting that the outcome is what the law was trying to regulate, and so the mechanism used to achieve that outcome is not important.
An analogy that would be more fitting would be to say that it sounds like applying an 1890 law against telephone harassment to an harassment that took place over a cell phone.
I see the Kagan quote as utterly rational. Concentrating on the mechanism rather than the result is like saying it is OK to eat the meat of a deer if you capture it in a trap and then kill it by slitting its throat with a blade that has been blessed by a priest, but it is not OK to eat the meat of a deer if you kill it by an arrow shot.