Perhaps not that specific option which controls some smaller facet of sharing and recommendations, however but it's definitely the case when you turn off syncing "Web & App Activity" with the Google panopticon.

Where the history would usually be, there's just this nagging message:

> To see your home and work, past searches, and other suggestions tailed for you, turn on Web & App Activity.

...Which, as mentioned already, misleadingly implies that local-history features are difficult or nonstandard.