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I've worked in the area of so-called advertising law for many years and dealt with any number of these kinds of issues. Glenn, welcome to the 2d class status known as "commercial speech." Were we to litigate, we would no doubt be able to convince a judge that your ad has the same legal protection as editorial content like the Times' piece. However, the executives, editors and managers of media companies instinctively view the ad the same way they look at an ad for soup -- inherently less worthy of First Amendment protection. And since they are embarrassed by the ad and afraid it might actually impact their business negatively, they will fight to keep it off the air.
Getting in front of a judge would help, plus result in valuable free media to boot. It's something to seriously consider...otherwise, welcome to the back of the First Amendment bus.