My guess is the RF tech is a lot easier to deploy when you can plan for some percentile of peak utilization, rather than 1:1 with the user base. Even then, they'd undoubtedly face legal challenges, so they must have made the judgment call that the odds were on their side. Which may have been a reasonable conclusion. A lot of the judgments were actually on their side until the circuit split and the final Supreme Court decision.
After all, one wouldn't imaging that leasing an old-school aerial antenna would be a legal issue.
It was a hot topic on HN several years back. I may be biased, as my wife did PR for Aereo through the firm she works for. But I definitely buy the logic that what they were doing was technical a private performance.