That's interesting. I was reading their licensing compliance FAQ at https://min.io/compliance and it doesn't allude to that; in fact it suggests that for instance calling a REST API doesn't imply derived work (modulo the specificity piece), referencing the GPL. The omission of the over-the-network AGPL provision is notable. I wonder if it's obscure on purpose?
MinIO has taken (and still is taking) contributions without CLA, so they likely don't even have the ability to sell license exceptions.
They seem to have at least fixed their compliance page. It used to read:
"If you are an Original Equipment Manufacturers, a Reseller, or an Independent Software Vendor that combines and distributes commercially licensed software with MinIO software and do not wish to distribute the source code for the commercially licensed software under GNU Affero General Public License, Version 3.0 (AGPLv3), you must enter into a commercial license agreement with MinIO, available at https://min.io/pricing."