But it does. If you get a new android phone and log in with a google account then it updates your browser history on chrome. Which could only be done if your non-incognito history is stored in google's servers.
Oh, I forgot about that - that feature wasn't available when Chrome was launched.
To be fair, that feature also isn't very hidden; the sync settings let you turn off history sync or use a sync passphrase which prevents Google from seeing your browsing history.
Microsoft was caught with their pants down returning google search results to microsoft via internet explorer. They call it "a signal" for bing. The difference between google and microsoft is microsoft isn't as forthcoming regarding what information they retrieve. No dashboard to browse everything microsoft tracks... You just have to trust microsoft. Good luck with that.