Earlier quoted context omitted.
That doesn't sound like him :) Do you have a reference/quote for that, out of interest? In the past it seems like he's been skeptical[0] of providing user data to third-party services. [0] - https://www.theguardian.com/technology/2008/sep/29/cloud.com...
This was from a private email exchange, but you can look at how he's soliciting a FOSS Google Docs client as evidence that he'd be fine with a FOSS interface to a proprietary service. Additionally, https://www.gnu.org/philosophy/javascript-trap.html makes no mention of proprietary backends being harmful to user freedom, only obfuscated (unauditable) frontend code.
OK, but the later essay https://www.gnu.org/philosophy/who-does-that-server-really-s... does.
The proprietary backend is providing a network service, the question is: to what degree is that service being used as a software substitute?
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My own opinions on RMS' opinions:
The essay I linked is from 2010; don't get too hung up on specific examples, things have changed since then. The Facebook of 2010 was fairly usable as a dumb service without being a software substitute. It was possible to consume your news feed via RSS, and perform your own sorting of it (for example).
That said, I do think that RMS has taken a rather naive view of which services are pure services, and which services are software substitutes. I can see how many things can reasonably be conceptualized as a pure service... but also, they could be replaced by software. If you could use software as a service substitute, then surely the service is a software substitute. And part of this changes over time, as people figure out how to replace more things with software. (Based on personal (mailing list?) communication regarding DDG vs YaCy vs Searx as the default search engines in FSF-endorsed distros)
It should also be said that RMS refines his views change over time, and that he often doesn't do a good job of acknowledging that they've changed, instead doing a sort of "I've always had this wisdom" thing. Years ago, he had a bit about how people would ask him about "free hardware", and that his answer was that the concept of free hardware didn't make much sense, as you can't copy a piece of hardware the way that you can a piece of software, and that having the source files for hardware wasn't very important. Then a few years later, consumer 3D printing and home manufacturing started to take off, but he held on to his old position. Then a few years later, he came around, and he had a bit in a talk at LibrePlanet about how free hardware was obviously important. So don't give old statements by him too much weight--his views change in response to new information and developments (as they should).