The advertiser would not be the responsible party any more than the ux guy, the graphics people, front-end, back-end coders, dbas, and network people who were involved in putting up the website.
It's the management that cleared the copy who is responsible.
First lie. (not saying you - but in general) Free market capitalism == caveat empto.
Second lie. There is no free market solution to thieves. A thief is not only a person who puts a knife to your throat but someone who claims this product is x when it really is y.
How would this work? There would be companies (and organizations) whose sole purpose, and main source of revenue would be in checking that a claim is truly a claim. If you are interested there are tons of articles and white papers dealing with this.
I'm not an anarcho-capitalist but if there's one thing that community does well is explore this particular issue.