The AGPL is exactly the same as the GPL, except that if there is a button to click to download the source code of the program, you are not allowed to remove that button.
If the Program as you received it is intended to interact with users through a computer network and if, in the version you received, any user interacting with the Program was given the opportunity to request transmission to that user of the Program's complete source code, you must not remove that facility from your modified version of the Program or work based on the Program, and must offer an equivalent opportunity for all users interacting with your Program through a computer network to request immediate transmission by HTTP of the complete source code of your modified version or other derivative work."
That last part--"derivative work"--is somewhat the rub.
If that part of the informal FAQ worries you that it might be interpreted in some strange way, just look at the actually license and read it.
Notwithstanding any other provision of this License, if you modify the Program, your modified version must prominently offer all users interacting with it remotely through a computer network (if your version supports such interaction) an opportunity to receive the Corresponding Source of your version
The definition of Corresponding Source code is listed earlier in this HN thread.
