Did Gary Becker prove that advertising is informative?

So claims a NYT obituary for John Kenneth Galbraith.  CrookedTimber and Brad DeLong question whether such models should be called "proofs."  Fair enough, but neither does the obituary correctly represent Becker’s theory of advertising.  As I understand Becker’s work (with Kevin Murphy) on the topic, individuals consume "social images" or "self-images."  Having Nike shoes gives you the "benefits of being cool" if a) you actually have Nikes, and b) the ad links Nikes to a cool image for your relevant peer group.  The standard economic theory of complements then applies for analyzing ads.  Under some conditions, advertising can be a "bad" for consumers, not a "good," and advertisers will pay consumers to watch ads.  Furthermore ads will present images and cultural linkages, rather than substantive information in the traditional sense.  This generates some Galbraithian results, but without requiring that consumers are "tricked" or even "persuaded" into a particular point of view.   This is not a proof; I think of it as an existence theorem that advertising can make corporate sense, and sometimes be socially welfare-improving, yet without being very informative.

Keep in mind that Becker titled his 1998 book Accounting for Tastes, a concession to the Galbraithian way of thinking.