I'm not sure any single company could have an outage that would take out SMS globally, but RCS is presumably more centralized.
RCS was designed and specced, by GSMA, as a telco run decentralized system that would replace SMS as like for like; but there were only a handful of rollouts. It's really only gotten use as Google pushed it onto Android, using their RCS server; recently iOS started using it although I don't know what server they attach to.
Since RCS is basically the 5th wave Google IM, it's no surprise when they have a major outage, RCS is pretty much broken.
According to Wikipedia, only the carrier's RCS server is used [1]
[1]: https://en.wikipedia.org/wiki/Rich_Communication_Services#So...
From the end user's perspective, if the carrier didn't use Jibe RCS, it simply wouldn't work well.