This gets into the long history of the GPL versus the LGPL and lots of legal battles in the text of those licenses and in the interpretation of the text in those licenses about the differences between types of "distribution" ("mere aggregation" versus "linking" versus "bundling" versus "inclusion"). In all but the "mere aggregation" case, the GPL is considered to be viral, and the LGPL relaxes that in some more "linking"/"bundling" scenarios.
The AGPL to do its work has to close the "mere aggregation" "hole" in at least some cases, which alone makes it "more viral" on the spectrum of GPL licenses. That's before you get into problems with how the APGL defines "some cases", in that it doesn't do a great job so no one knows exactly how viral it is because it will take court cases to sort out its bad wording on the subject.
(For instances: 1) The AGPL is intended to expand to include "running it in a SaaS environment" yet the way it (doesn't) define "SaaS environment" is so poor it could mean running it anywhere. 2) The AGPL was written by a PHP company and so a lot of the definitions, distinctions, and clauses from the GPL regarding the differences between binary and source distributions were struck out. Because most of the known legal definitions on "mere aggregation" with regards to the GPL hinge on those distinctions we have fewer and fewer ideas of what "mere aggregation" means with respect to the AGPL, and it again possibly implies that the AGPL's virality is potentially unbounded, that their "some cases" is intentionally or accidentally written as "all cases".)
The AGPL to do its work has to close the "mere aggregation" "hole" in at least some cases, which alone makes it "more viral" on the spectrum of GPL licenses. That's before you get into problems with how the APGL defines "some cases", in that it doesn't do a great job so no one knows exactly how viral it is because it will take court cases to sort out its bad wording on the subject.
(For instances: 1) The AGPL is intended to expand to include "running it in a SaaS environment" yet the way it (doesn't) define "SaaS environment" is so poor it could mean running it anywhere. 2) The AGPL was written by a PHP company and so a lot of the definitions, distinctions, and clauses from the GPL regarding the differences between binary and source distributions were struck out. Because most of the known legal definitions on "mere aggregation" with regards to the GPL hinge on those distinctions we have fewer and fewer ideas of what "mere aggregation" means with respect to the AGPL, and it again possibly implies that the AGPL's virality is potentially unbounded, that their "some cases" is intentionally or accidentally written as "all cases".)