It's a simple extension of the spirit of the GPL and of free software to software that is ran on the servers of someone else on behalf of the actual users of the software. The GPL has always sacrificed the freedom of creators of derivative works to distribute their derivative works under different licenses in order to protect users. The AGPL is a natural extension of this to software that isn't normally technically "distributed" to its users. The GPL fails to protect users when the code in question is used to create SaaS applications. The AGPL fixes this weakness in the GPL. It's not "RMS really compromising his principles"; it's the FSF really fixing a bug in their implementation of their principles.
The GPL's mechanism fits neatly within the bounds of copyright law, as it hinges solely on distribution. The AGPL goes beyond that -- you must agree to it to run the program, which makes it a naked EULA.
Making one's source available is quite often not simple at all, and in the case of nearly all SaaS apps, completely useless even to developers, much less the end user. The frontend CRUD code is disposable -- the server infrastructure, the network effects, and your fucking data are what matters. RMS doesn't understand this at all, probably because he doesn't use any such applications.
How does other people seeing the source code of a program prevent you from running it for some purposes?