That's the point of the license, that if you use the software for building a broader one everything for running it shall be warranted to be libre too.
GPL only requires that if you publish the software, but AGPL goes a step further and requires it if you use the software as an Internet service.
That's why the Imageflow Server has dual licensing, for those who don't want to publish the code. Then you pay for it.
The GNU licenses say:
All the source code needed to generate, install, and (for an
executable work) run the object code and to modify the work, including
scripts to control those activities.
However, it does not include the work's System Libraries, or
general-purpose tools or generally available free programs which are
used unmodified in performing those activities but which are not part
of the work.
For example, Corresponding Source includes interface definition files
associated with source files for the work, and the source code for
shared libraries and dynamically linked subprograms that the work is
specifically designed to require. Such as by intimate data
communication or control flow between those subprograms and other
parts of the work.