I think one could make a not-entirely-unreasonable argument that by streaming the DVD you're making an unauthorized copy of the data on it.
What are they doing, after all? They read bits off the DVD, make another set of bits which contains essentially the same information compressed, and transmit it to a remote location. Sounds like making a copy to me.
How do you play a DVD on a modern TV? HDMI. Same exact type of "copy".
If you "rent" the player from them as well as the movie, then it is the same fair use that allows you to play a DVD on your tv.
HDMI, or whatever--even via analog makes up to 5+ copies just to get out of a modern TV (D->A from your player, A->D to your TV, several copies and augmented copies into a buffer handling picture processing, scaling, and motion smoothing, and then pixel elements in an active matrix LCD store their values in embedded transitors, and the physical twist of the liquid crystals is another copy, not to mention the light travelling through the air, the copy your retina makes as it scans the TV, the persisted gradually degrading copy that makes it into your mind)).
The difference being that those copies are authorized by the copyright holder and this one is not.
You're right in that that's an obvious counterargument. I don't know how it would play out in court. I don't wish to argue that my "this is a copy" argument is undefeatable, but I think it's sufficiently plausible that this is what the copyright holders will argue when it comes to trial.
And this is why geeks make bad lawyers. "Surely," they say, "if A is allowed, and if by a set of trivial extensions we can turn A into B, then B must also be allowed". But the law looks at A and B and sees two very different things, draws a hard boundary which might not make any particular sense, and doesn't care about careful analytic arguments.
Here's another copyright problem. If I have a party and screen a DVD to ten people, that's fine. If I have a party and screen a DVD to twenty people, that's fine. But if I have a party and screen a DVD to five hundred people, I'm holding a public screening and it's not allowed under the terms of my DVD license. How can this be? It just is.
That's a separate issue though. Screening a single physical DVD to a party of people simultaneously is illegal.
But me connecting a really long cable to a DVD player and connecting it to my TV. There's no way that can be illegal. There is no A and B in your argument. There is 'A'. Connecting a DVD player to a TV using a cable.
Oh, that's easy. This company claims that the user is the only thing legally involved, and they have merely provided tools which the user is using to watch DVDs that happen to be physically located elsewhere. Therefore they are entirely uninvolved and therefore can't be said to be in violation of anything, indeed, they shouldn't even be a party to the suit; if the movie companies want to sue anyone, they will claim, it should be the end-users. The companies will claim that this is not simply a tool and that the company is actually involved in serving out streams that they do not have a license for and are therefore violating copyright.
The reason why this will be an exciting lawsuit to watch is not that the arguments are subtle or difficult to predict in advance, it is that they are both oqually correct. What's wrong isn't either of these arguments, it's the foundation of law they are built on, which simply can not handle this conflict. I've been waiting for this one to pop up for years. There are numerous other minefields like this waiting too.
BTW, the temptation to physical metaphor is strong here, but as always should be resisted. There are no physical metaphors that adequately capture the Internet and this is no exception. No, this is not merely like stringing a big wire across the internet, there are critical ways in which that differs from this situation. For instance, when I physically own a DVD it isn't possible for anybody else to know what I'm watching, and if the manufacturer goes out of business nothing happens. (Remember, it only takes one relevant difference to sink your argument-by-metaphor, which is why it's such a terrible argument technique and basically should simply never be used for Internet issues.) On the other hand, this is also quite clearly not identical to Netflix-style streaming, as it also has relevant differences. (So, from another point of view it is fair to say both arguments are also equally incorrect.)
You can argue the ethics quite fruitfully, but I believe the legal answer to this can only be said to be undefined. There is literally no provision for this anywhere in copyright law, in fact copyright law is fundamentally built on the premise that it is possible to cleanly separate copyright issues into various distinct "domains" (books, music, movies, etc) which don't cross or interact. As computers and the Internet blur these domains together and create some news one, the law really can't deal with this. The system is not built to handle the idea of you owning something and consuming it from a distance, either, the particular undefined thing this company is trying to wiggle through.
(Which won't stop a ruling shutting these guys down this time, but at some point the law is really going to have to address this problem head on.)
Unfortunately I think you're right that there will probably be a ruling that just shuts them down. Having worked for a company that was sued by large media companies and lost, I can say that while the suit was extremely complicated, the individual details were mostly glossed over as irrelevant. (for instance, the difference between a website and desktop software) The court knew where it wanted to end up, and wasn't all that concerned about how it got there.
As hackers, we'd like to think of the legal system as a big piece of software that responds consistently to commands, but for better or worse it isn't.
I expect something like forbid playing rental dvds on players more than 10 feet away from the TV... This is going to be sick.