[Whitestrake]

Using "in-band" here doesn't really follow from a technical understanding of the term; the TCP connection is the channel, and anything sent over it (such as an entire HTTP request/response, including headers) is "in-band".

Out-of-band would be a phone call, or perhaps an email - an entirely alternate method of communication.

Transparency to a user (via the client, i.e. browser) isn't really relevant, from a communications standpoint, to whether or not data is considered "out-of-band". Given the subject (APIs), you're not likely to be browsing to these anyway.