I'm not quite sure I follow. The AGPL mirrors the GPL, with an extra proviso that accessing the software via the network constitutes "use" if the binary, not "distribution" of the binary. Under GPL, the mere use of a binary does not require the availability of source.

Example: a student uses a GNU/Linux computer at their university computer lab. She runs the unmodified "tar" command from GNU Coreutils, which is GPL licensed. She is not entitled to a copy of the source from the university, because execution is a "use" of the binary on an already-provisioned machine, not a "distribution" of the binary.

Example: a student is given a software assignment from her professor, along with a .7z file containing old versions of "tar" that contain bugs, all GPL licensed. This is a distribution -- as in, a copy -- of the binary, so she is entitled to a copy or link to the source from her professor.

The first example helps explain what the AGPL adds, in the context of network use. Consider what happens if the university actually modified the "tar" command installed on their machines. They still would not have to distribute the modified source to the students, because students only execute ("use") the binaries. But with AGPL, use of modified software obliges source distribution.

Phrased another way, AGPL has every guarantee that GPL does, but adds another obligation for modified use via a network. Unmodified use does not require source distribution, under both GPL and AGPL.