I think you should simply write to them and request their permission to use their contents as API. It might even get them some backlinks and PR, and they could also charge for the services while you have contents for your site. Anyways, it's a win win for both of you.
Talk to them.
I
think this
COULD BE solid advice,
IF you elaborate on who {"
them"} would be.
For example, if it's a
legitimate (I make no assumptions) 3rd party website who has the permissions of the actual content owners to host their content, and he's asking
them (the 3rd party website), then that's one thing.
However, if it's not a legitimate (again, no assumptions) 3rd party website who fails to have the permissions of the actual content owners to host their content, and he's asking
them (the 3rd party website), then that's something else.
And if he's referring to "them" as being the actual content owners if he can link to a 3rd party website (either with or without said 3rd party website having express permission from the content provider), then these can be quite different scenarios, as well (one advised and one maybe not).
I preface all that with I think, because I honestly don't know and would hate to give you a wrong answer on this one. As boring and not cool as this advice may sound, I'd say your best bet would be asking an attorney. You may be able to find one for relatively cheap, online (do your due diligence, of course), but just know that each content provider may have their own forms of ToS, so I don't know if the attorney would want a separate "ticket" for each instance, or if you can group all the content providers you plan to use, and lump them all into one single request. I don't know. But, I think to CYA (Cover Your A.....) and if it's going to be a website you're going to care about and want to maybe some day build into something greater, then starting with your best foot forward would probably be a solid approach.
Heck, if you play your cards right, the content owners may in the future let you host their movies, yourself. Of course, assuming you're website is successful by then, then surely you'd have the budget for it. You may then even check out some great hosting solutions.
I hope this helps. Good luck & May 4th.