The "without any proof" part can be debunked even without the deep data, just looking at sales figures and conversion rates of personalized ads vs traditional "scatter-shot" approaches.
Who are these folks doing this "scatter-shot" approach? How do we get some insight into their practices?
The major company doing context sensitive advertising nowadays is Amazon. When you search on Amazon, they display relevant "sponsored" products that are clearly labeled as such.
So how is Amazon's "context sensitive" advertising business doing? By most accounts, pretty good actually.
The real problem in my opinion is the lack of competition to the "personalized" approach. Everyone (except Amazon) just accepts "personalized" as the default --- mainly because there is no credible, large scale, organized, generally available alternative to compare it to.
I don't think I want to argue againsr these ads on the basis that there's some alternative form of advertising that's more effective.
The problem is with data mining and tracking and nudging behavior. I want the things driving my behavior to be originating from my own intentions or from my preferred sources of inspiration (e.g. friends, family, media I'm most interested in consuming.)
You'll never be able to fully control the range of things that influence you, but you can still be intentional to a meaningful degree. For me that means supporting free and open source culture, and using subscription-based model rather than an ad-supported model for content. I'm not perfectly consistent but I am somewhat, and I think I'm operating from a coherent vision of what I believe my interests are, which is no small thing.
Amazon is not a good example of contextual ads, though. It doesn't generalize:
1. You can easily argue that these "context sensitive" ads are actually personalized ads: They're personalized based on the search query you just made! Amazon context ads are the same as Google/Apple App Store "context ads". Suppliers are paying for higher ranking.
2. It's a shopping website! Of course those context ads are going to have high ROI because they're showing an ad relevant to the thing you're shopping for!
When people talk about context ads, they mean "Why doesn't Facebook or the local newspaper use context ads?" They don't mean "Why doesn't Target put up a coupon for beans in the beans aisle?"
Not an apples to apples comparison really. Amazon owns the entire user journey on its platform, which the "ads" are an integral part of. They are not analogous to Google showing you ads in banners and searches for target pages it doesn't own, on platforms it doesn't own. If you want to compare Google to those who actually advertise with the scatter-shot approach, you compare them with traditional advertising providers - ad spaces on TV & radio channels, billboard companies etc. That'd be a fair comparison because Google is also essentially a seller of ad spaces it "rents" from other websites - just in this case those ad spaces can simultaneously show different advertisements for different clients to each user, based on that user's best-match profile. It's a no-brainer that Google's approach will yield more leads.
There are smaller examples too. The Register was one such example the last time I checked. They sell space on articles and also run Sponsored Content features.