That'd avoid all the "breaking the DRM", "modifying the data", etc.
As provider you just offer a device that loads dvds from a user's in-datacenter storage cabinet into their in-datacenter dvd drives, and rent them a dvd drive.
That might be complicated enough to avoid the whole "performance" interpretation
Right. Aereo notwithstanding, one way around this might be to set it up like MP3Tunes[1] where you're a specialized digital locker service. The "fixed" "tangible medium" should originate with the customer, and a transfer from the customer-controlled copy to the business should be involved (rather than the other way around). With a large enough physical presence, you could get this down to pizza delivery time frames and/or Redbox levels of friction.
1. contrast with mp3.com
There is, strictly speaking—it's part of the exclusive rights that Title 17 lays out for copyright owners[1]. It's just that (a) it forces you to be in the business of doing the rentals yourself (you don't get to just point at someone with an interest doing rentals and dictate terms to them, sans contract), and (b) even if you're doing your own rentals, if you're also selling copies, then there's nothing stopping someone from doing an end-run around your rental business by just buying a copy from you and doing things their way with that copy.
(Granted, this doesn't make the person you were replying to any more correct about what they meant when they said you couldn't do this.)
1. "distribute copies [...] by sale or other transfer of ownership, or by rental, lease, or lending"
You can't buy a DVD and charge tickets to see the DVD played by you. You can't stream the DVD's contents over the Internet. But you can absolutely rent the DVD itself.