This is why I don't understand copyright law. Aren't data facts? Facts can't be copyrighted, right? Where a business is located is a fact. How can they say how someone else can use that fact?
Facts are not copyrighted, but a collection of facts as such may be copyrighted, assuming there is some creative activity involved in compiling the collection. So, a list of the most common English words would be copyrighted, since there is creative effort involved in deciding whether a word is common.
IANAL, but I think you're right. They really can't tell you what to do with public data even if they provided it to you, because as you said you can't copyright facts. Feist Publications vs. Rural Telephone Services is the most relevant case:
It gets hairy though because you are agreeing to their terms of use in return for the API key, and I'm not sure how that factors in. They're well within their rights to refuse service to you, but if you were able to scrape their data without agreeing to their terms, it may be legal.
Of course there's a million other places to get this data, and I'm not suggesting you scrape theirs. But I don't think there's anything stopping you legally, just some FUD in their TOS.
Would be very curious to hear from the site owners on this topic.
