Well, you're in the ballpark. I might be wrong, but I've heard they're not averse to the idea of open sourcing Borg and Omega (it wasn't that long ago that the Borg paper would have been nigh unthinkable, interestingly), but the litany of Google specific stuff that is baked in makes refactoring for public release a nonstarter. It's a huge codebase with lots of little tendrils to other internal infrastructure.

Anyway, one needs an on-ramp to containers on Google Cloud. And one can't open source the one that one has, which despite being nearly mature enough to own a driver's license, wouldn't really fulfill the precise need that Kubernetes fills without some frontend work. So one writes Kubernetes. An almost entirely different fundamental architecture, by the way, so it's interesting for those who've seen both to compare.

In other words, you're not entirely off the mark even with the generalization.