It's funny how your line of argument can seem so obviously accurate to one person (like myself) but so obviously wrong to another (like whoever has downvoted you here). FWIW, I think your distinction between advertising and dissemination of information is a good one.
Those who disagree might nevertheless be surprised to learn that recognized protection of commercial speech (i.e. advertising) by the 1st amendment is only a fairly recent legal development. I would suggest to anyone interested in the topic to revisit the arguments in Virginia State Pharmacy Board v. Virginia Citizens Consumer Council. This case, from the 1976, was a key stepping stone that paved the way for the rampant drug advertising that we have in the U.S. today. In fact, the lone dissenter, the late Justice Rehnquist, foresees precisely this outcome in his opinion, predicting almost the exact "talk to your doctor" phrasing that we have become so accustomed to decades later. By contrast, the majority justices sound like nothing other than hapless and naive dupes of an astroturfing campaign, speaking guilelessly about issuing their decision on behalf of "consumers of prescription drugs" and their right to receive "information". I doubt that they anticipated anything remotely approaching the ravages that, for example, the opioid epidemic would bring.
It's easily on my own personal "top ten" list of bad Supreme Court decisions.