It would not even make sense. Since you do not even always know what license the thing has you are connecting to. And not even the fsf sees it that way.

Sure, if you're connecting to a service using AGPL, the service operator must offer the source along with a copy of the license.

I'm no lawyer, but unless the software in question makes an exception for the particular API, I wouldn't feel confident.

Or what is the distinction here?