In iText's case this is not a misrepresentation - itext core is not a product like elastic or something that you interact with over the network, it's a library

In iText's case this is not a misrepresentation - itext core is not a product like elastic or something that you interact with over the network, it's a library that you build into your program. And yes, in this case you would be bound by the license to release the programs you build it into, to the clients who interact with it over the network. The handwavey part is - what is "the application"? And they are not going into specifics there - it is, of course, only the application that you build it into. It doesn't virally extend to other things that interface with it over the network, and they're not going to say that part. You naturally can thus build a minimal "wrapper app" that just provides this library-as-a-service according to some interface, so that you didn't have to release your whole program, but, it is not a misrepresentation that if you use iText core then at least this program will be bound by AGPL and must be distributed.