The whole point of _performance_ advertising is that it's effect is _measurable_. If AirBnB spent $500m+ on performance advertising, they should be able to trace that back to an exact amount of revenue. If you are a brand in this scenario, you can conduct split tests by sampling the conversion rate of users from advertising vs non-advertising. Again, it should be simple to see if the conversion rate for users targeted via advertising has increased or is unchanged.
In the branded search examples, again, as an advertiser, you can see what searches are associated with your leads. While you do have to compete for attention on your own branded search (to compete against competitors taking the slot), you should also be able to recognize unbranded terms which drive conversions for you. Again, assuming this is actually _performance_ marketing, you would be able to look at the cost of these placements and the ROI, and the impact would be measurable.
The rest of the article is largely composed of straw-man arguments that imply the results are not measurable, when in fact they are (if done right).
disclaimer: I'm the CTO of a performance marketing platform. The vast majority of conversions on our platform happen same-session. There's a very easy way to measure this effect -> pause your campaigns and immediately see conversions fall.