Well, that's not strictly true. But the way advertising convinces customers is often far less direct than you would expect.
It's about name recognition so potential customers will remember the name and be more inclined to buy that product instead of a competing one. In this case, negative publicity can actually be beneficial, paradoxically, as long as the potential customer remembers the name but not why they remember the name. It also goes to reminding customers that a brand or product still exists, which is why you see established brands advertising periodically. This applies to goods *and* services. Name recognition is why those weird commercials that make no sense whatsoever but end with a shot of the product and a name card exist. Also some of those ad campaigns that tell multipart narratives. Etc.
It's also about creating buzz around a brand or product. This hasn't historically been primarily aimed at end customers. It is often actually aimed at buyers for supermarkets, department stores, and the like. After all, the end customer can't buy your product if store they shop at doesn't sell it, right? So a lot of advertising is aimed at the people who choose what gets stocked by shops to get them to stock the products to customers can buy them. With direct online sales, this is less important these days, but it still plays a role for products that might be stocked by shops. Of course, this also doesn't apply so much for services (professional or otherwise).
And, yes, advertising does need to convince the end customer that they want to buy the product in many cases. Especially for luxury goods or services. Here, simple name recognition is probably not enough, especially when you have competition. In that case, you have to give reasons why a customer should choose your product or service. But you also need to advertise to people who don't already have your product or service, and that's hard. Which is why a good ad campaign serves all three goals: name recognition, buzz generation, and convincing the customer to buy.
I think a lot of companies either forgotten or never knew what the real purpose of advertising is. They got in a mode where they think throwing more money at an ad campaign will make it perform better. And, of course, advertising companies benefit from that so they won't set their customers straight. Mix in a liberal dose of not recognizing how the market has changed with the advent of the interweb, and you get massive overspending on advertising with little or no benefit.
Basically, cutting an advertising campaign that is poorly implemented and/or poorly targetted leading to no change in outcome is hardly surprising.