An interesting aspect of Aereo's model is that they attempted to circumvent these regulations by leasing each customer an individual antenna which they could access remotely. They maintained "antenna farms" full of tiny antennas.
There wouldn't be loopholes if the law was consistent, and I would argue there is no 'spirit' in such a confusing set of rules.
They might also need to sell you a short-term lease on that particular drive bay, so that you are playing the DVD in your own home too.
First sale doctrine covers rentals, but having good relations with studios to get supply of new releases often influences rental establishments to avoid buying discs at retail to rent out. (But, RedBox will sometimes do it)
They buckled from pressure from studios and agreed to stop for the reason you gave.
It kind of seemed at the time that they used their right to do this as a negotiating tactic in getting better prices from distributors.
Kind of sad it got killed off :(