As someone who leads an analytics team in the advertising industry I have to say this title and the studies they are referencing are not accurate to the entire industry at all.
Advertising absolutely works when done right. The effect on brand consideration, shopping behavior, and incremental purchase value can be quantified. The most sophisticated advertisers spend a lot of money to accurately track and ensure their campaigns are lifting their desires metrics.
Now to the eBay study they reference. That study is specific to eBay, a large brand that has spent hundreds of millions a year on advertising for many years and is a top web property visited by a significant percent of the online audience. For eBay it turns out brand search marketing largely does not have a contribution as most of their shoppers are likely going to buy anyway.
Trying to generalize that to a brand that did not have the amount of equity, natural SEO rankings, and established shopping behaviors would be foolhardy. Additionally if you dig deeper into the eBay study they did find a positive effect for the small percent of users that are new shoppers to eBay. They just happen to be a relatively small percent of the audience reached with the spend given the large size of eBay.
In the digital space there is a huge variability in performance based on the type of ad, the nature of the targeting, the product being advertised, the creative message, etc. Trying to generalize to all online advertising without controlling for the kind of brand, product being sold, current marketing positioning, and campaign objective seems a bit naive.
In our work we find huge variability in performance even within the same web property dependent on the placement of the ad within the site and the unit being served. We measure how long the ad was on the page, how many users actually hovered over it in view, and then the incremental lift of exposed users compared to control group. Turns out if you properly optimize to maximize true ad viewing and engagement you will see lifts in brand response, digital visitation, and shopping metrics compared to the control.
In fact I'd much rather have money for digital advertising any day over old fashioned ads with the limited tracking possible. I know how many people saw our spot on the YouTube home page, how long they spent interacting with it, and can tell you exactly what they were interested in. For that TV spot I don't know if you were watching, skipping, going to the bathroom, looking at your phone, or any number of other factors which could diminish effectiveness.
TLDR; online advertising works when done correctly and absolutely can be measured