The Short Answer:
The Long Answer:
The derivative definition is based on copyright law and not a license, and I can't see how a remote web services interface could ever be construed as anything other than separate from the server involved.
You are interacting with a service, not including it in your code.
A service provider MAY be able to constrain you (and your code) with a CONTRACT, but this is a LICENCE, and it shouldn't be able to re-licence your code.
An API (may) have patentable components, but the implementation of a REST service means that any code could interact with it, so it doesn't depend on copyrightable things like Java interfaces etc (or a non-trivial YML).
Although due to a recent court case between Oracle and Google over Android, an API (probably doesnt matter if it is over a remote interface) can be copyrightable, thus the service provider can constrain your actions with respect to that API. Particularly if they introduce complexity in order to force copyright infringement in order to use the interface. (Update: This ruling was reversed by the Supreme Court on April 5, 2021.)
All remote access
to this software must always
include this haiku.(c)
From memory, AGPL is about forcing the re-licencing when a derivative of the source code is offered as a service, but I couldn't follow the wording of license when I tried.
Please note: IANAL and my memory is shaky.
I looked again at the AGPL Licence, and I don't see the constraining language myself, except in the preamble.
Does a report written against a AGPL licenced library (such as iText):
- Require the database structure (usually remote) to be licenced as well?
- Does that include the data?