Source: I am the former Chrome omnibox owner. You can find the relevant code for this starting at https://cs.chromium.org/chromium/src/components/omnibox/brow... ; look for how GetDefaultProviderURL() works and when that query is sent. You can also watch packets with your favorite network analyzer.
I agree it would be nice to let people configure this (see comment 12 on that bug), but we're pretty careful about getting privacy right (despite wide-ranging internet claims to the contrary) and "falling back" to Google in that case would be a pretty major gaffe.
We haven't always been perfect. When we first launched, for example, we didn't exclude some cases from suggest querying that we should have, and that was my oversight. I can't remember the specifics (things like https:// URLs or input while in incognito mode, IIRC) but I landed a patch a couple days after the 2008 launch to clean it up.
The Chrome team as a whole is very privacy focused. There's a lot of people in public (including in this article's comments) who think Chrome is some sort of Google data collection device, but having seen things from the inside, I would trust Chrome with my data over any other browser. It makes reasonable tradeoffs by default (e.g. not enabling features like sync or server-side spellcheck that tend to send more data), and what stuff is there that people might not want (e.g. omnibox server-side suggestions) can all be easily disabled.
See also https://en.wikipedia.org/wiki/Google_Chrome#Listening_capabi... , which is a reasonable summary with more detail than what I've given above. For full details, see https://www.google.com/chrome/privacy/whitepaper.html .
It's the complete opposite to that, and you said it yourself. Their aim is to quietly retain/recapture users while keeping antitrust at bay, and they did well precisely in not publicizing it.
I suspect people that actually care about privacy aren't using Chrome though.