"But given that advertising does change sales numbers, that cannot actually be true."
What metrics do advertisers have to gauge the effect of advertising?
Say you advertise to 100 people and one of them comes along and buys whatever it is you're flogging. What do you know about the other 99?
You may assume that they're not in the market for the product, that you found the one who was and therefore you were completely successful.
This, however, assumes a lot. There might have been 10 people in the market for the product who'd have found their way to you but your ad pissed off the other 9 so that they've gone elsewhere.
You may be a little less happy with this outcome but it could be worse, 5 of those 9 might have been regular customers who are now somebody else's customers instead.
Does the advertising industry do any research on this? I suspect not - it might frighten off their clients. I remain convinced that the only products and people to whom the advertising industry successfully advertises are themselves to the clients.