If they can change the terms whenever they want, you don't really have any protection at all. So you are likely going to be screwed if the big company ever wants to stop you from doing this. The solution is to either make sure the big company is happy with what you are doing, or line up alternative sources for your data. A lawyer won't help you.
Is whatever you need to do a one-time thing, or ongoing? If it's one-time and you're worried they'll change something retroactively, they probably can't but you should check with a lawyer just in case. If it's ongoing, you're probably screwed with that contract.
