You are right that that warning at the top of the AGPL text applies to the AGPL text, not the code to which the licence applies. Quite intentionally, the licence text is invariant, so all documents calling themselves the "GNU Affero General Public Licence" have to be the same.
But most of the licence is designed to apply to the covered code (rather than to itself). One such is s5c, referring to the distribution of modified source versions:
You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply [...] to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way
Another is s6, which says that the same condition applies to non-source-code distributions. The upshot is that you cannot relicence this code away from AGPL to any other licence, without the explicit permission of the rightsholders. While none of us can guess whether they will give this permission, their choice of the AGPL - traditionally the most copyleft-y of the copyleft licences - suggests to me that they won't.