Bill V,
I suspect, just like Netflix, Blockbuster, Redbox, Comcast, AT&T U-Verse, Amazon, and others, the company providing the Zediva paid service enters into contractual obligations with studios and other content providers to pay them back a royalty for each movie rented, or has some similar agreement.
You are right, though, that if they don't do that, then there would be legal issues. If, they DO do that, and I would think they would have to, then there should be no legal issues.
Also, as for the concept, this is in action on many sites on the web, by many providers. Though, a $1 rental (as championed by Redbox) is pretty novel in the online streaming rental model.
Thanks for the post.
TJR