Well, no, the OS is software on which, arguably, nothing is private. But you can put a different OS on a Chromebook, and apparently plenty of people who are concerned about ChromeOS -- whether for privacy or other reasons -- are putting Linux on them and finding Chromebooks a good way to get inexpensive (or not-so-inexpensive, in the case of the Pixel) Linux laptops.
It isn't any different than running Chrome on your other legacy platforms. Privacy comes in different forms. The content I place on my drive directly is private. Beyond that, it has the same privacy as your web browser.
It concerns me for reference.
The device is dangerous to say the least.
I wish Stallman would write about them as people might start paying attention to those of us who can see what is coming.