No, AGPL does not have any "special carve out". But in the section that is the difference from GPL (section 13, "Remote Network Interaction"), it clearly state

No, AGPL does not have any "special carve out". But in the section that is the difference from GPL (section 13, "Remote Network Interaction"), it clearly states: "if you modify the Program, your modified version must ..." [emphasis added]. So the extra stuff that differentiates AGPL from GPL applies only for modified versions of the software. For the rest, usual GPL stuff applies: if you distribute the binary, you must make the sources available, etc.