https://itextpdf.com/how-buy/AGPLv3-license
Not really AGPL, they just advertise AGPL and mean something else. Avoid.
I personally think the AGPL would win, but it's not something I'd be willing to enter a legal battle over.
You already know that the licensor has his own, idiosyncratic interpretation. He either misunderstands the AGPL (probably clause 7 par 3 b), or he’s trying to deceive you. Both cases can easily lead to hostilities.
“ If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. ”
https://www.gnu.org/licenses/agpl-3.0.en.html
I think the expectation here is that commercial users purchase the AGPL opt-out.
Imagine if Bic said you had to write their name on every page you used one of their pens on.
Back in the day FlowPlayer (a JavaScript component to play videos on the web) used additional terms per GPL section 7 to force users of their unpaid version to keep their mark intact in the UI or for modifications keep a "based on FlowPlayer" in.
I followed the discussion on this back then and the consensus seemed to be, that this is in line with what section 7 of the GPL allows. I think there was even a statement of the FSF, but I could not find it anymore.
Of course the iText case is different, but I believe section 7 (especially 7b) allows a way to add terms for attribution.