If these people read a bad news story about google, they will not know how to stop using google for any and all web access. A discerning consumer often opts to alter their product use under similar circumstances. They are dependent on a middleman because their understanding of the boxes they type things into does not reflect reality. This is what it means for a mental model to be "wrong".
The realized model of having two separate boxes could only ever be "wrong" in a moral or aesthetic sense. This is not the case for mental models, which are incorrect when they do not correspond to reality.
I think if we imagine that a user, having read some bad news about Google, will respond with "I'm never typing anything into that little search box next to my URL bar again" and isn't simultaneously a user savvy enough to respond to such news by reconfiguring their network stack to blackhole all traffic to Google servers, we're thinking of users that exist in such a small quantity that we could address their concerns by finding them, one by one, and teaching them how to edit a network stack.
The vast bulk of users would respond either by changing nothing about their behavior because all this stuff is inside-baseball to them, or changing their behavior by resetting their browser's search bar to some other target (for example, I can go into Chrome right now and remove Google from the list of search engines).
At this point, one really has to reach to conclude that awesomebars are bad for end-users without an ideology that doesn't reflect the average user very well at all.
The realized model of having two separate boxes could only ever be "wrong" in a moral or aesthetic sense. This is not the case for mental models, which are incorrect when they do not correspond to reality.