Not sure how you concluded that that was my assumption. To have a "unique position" is completely irrelevant. The point is that Google users are sticky and valuable because Google keeps them engaged, and knows more about the users, and so the ads can be more targeted and thus more relevant to the user. In other words, ads shown to Google users by way of Google's ad service are (theoretically) more likely to be acted upon. That the users stick around using the Google services for long enough to potentially see the ads is icing on the cake, and Google's services being as ubiquitous as they are doesn't hurt either. Whether there exist other services in the same position as Google's has no bearing on the intrinsic value of the user base.

On the other hand, your argument that Schmidt's post is "b.s." hinges on the assumption that catering to users is a completely separate business model distinct from catering to their direct revenue sources (e.g. ad publishers). It's not.