The thing about the "advertising doesn't matter" argument is that there are situations where advertising absolutely matters - when a company is just starting out and there's no way they can get organic referrals, when the public is unaware of their existence, etc.
Moreover, most companies started small at some point so advertising and maintaining advertising made sense up to a point.
And if we look at those companies where maybe advertising actually doesn't help, companies that have reached a level of success where organic referrals and public awareness drive most of their business. And they're ongoing businesses that probably reached that level through advertising and have money now to use for that.
But not only are they already advertising but they don't if their word-of-mouth/public-knowledge presence will last indefinitely, they don't know if just word-of-mouth would let them control their image, would stand-up against future competitors ads and so-forth. So, even supposing you could show advertising didn't offer any immediate increase in customers, continuing to spend on it doesn't seem to me as irrational as it sounds.