Why I have trouble trusting FSF

Ah, it seems like there is a difference between version 1 and 3 of the AGPL. Version 1 only requires that "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 [...]"; this was what I had in mind. However, version 3 does indeed require the code of any derived software to be shared when "offering access from a designated place".