It is not false in the context of the web being built on free software. The GPL is meant to prevent a situation where free software is used to create proprietary software that denies its users their freedom. In the case of web companies modifying free software and presenting their modified software to users as a web app, that is exactly what happens, and it is only because of a loophole that it does happen. The Affero GPL was created to address this particular loophole.
Along with the point you've just made, I thought about this after my last post, related to the difference between a tablet and the cloud. If a company changes the Linux kernel or an open-source application and includes it in their mobile device, they have to release the source on demand. As intended. (And there have been a number of high-profile cases in which companies tried to avoid releasing source.)
But if they change the Linux kernel or an open-source server utility and put it on their cloud server, they don't. An unintended outcome, and one that makes the cloud different than what came before it.
So I concede that the cloud is different, and it does affect the idea of open-source.
The line is drawn if and when a client machine downloads an open-source app from the cloud. If that never happens, then there's no requirement to release source.
