I wholeheartedly agree. Licensing is a complex topic of which I've read a good deal, and even within the Open Source communities there are usually a lot of misconceptions, so I like chiming in with less commonly pointed but very practical effects of it all, in case it helps someone to learn a tiny bit that day.

In this case the provider would of course have to comply with the AGPL and release their modifications as you mention, but it's important to note that No FOSS license protects at all against, for example, just offering the code as a service. It's the exact reason why Mongodb changed licenses and then a stream of commercial products started to change into "Source-Available" licenses in the recent past.