It is objectively true. AGPL does not meet the definition of free software, because it restricts the use of the software when modified.
The FSF pretends this isn't true by pretending that some uses are actually redistribution. However, this is too clever by half. Redistribution has a well-settled meaning, and allowing interaction over a network—unless it involves downloading the software itself—does not meet that definition.
The extra network clause triggers on modification, not redistribution.
Let's grant your definition of "redistribution" for the sake of argument. How does the license restrict your use of any modified versions of the software? Like, what specifically are you forbidden from doing?