What's the difference between a web API that provides data and one that's an interface to remote software? Seems like a blurry line.
If so, the company hosting it is providing a convenience. You can fork it, modify it, extend it as you like.
If not, the company can dictate how and when the service is used.
If they were writing against APIs provided by an open source library built on Overtone + Clojure (in some JVM-less form), I would hazard a guess that RMS would not have disapproved.