Simple solution: Show the tests!
There is no debate. You are misunderstanding what a "natural link pattern" looks like. How can you make such a general statement saying a site is better off with less than 5% targeted anchor text, without seeing their on site SEO and content?
If I am targeting the keyword "Dogs" and my content is 99% about "Cats", there is no way I will ever hit my goals for that keyword ranking unless I massively backlink using high quality anchored backlinks. Sometimes you need to force Google to go against their natural instincts to rank you for certain keywords, based on your anchor text.
If enough people are linking to you, saying your site is about Dogs, then screw the content, Google will believe its about Dogs. Prove to me something different. Don't just walk into a thread, call everyone dumb, then leave without trying to backup your statements. Especially when you claim about all of these "Tests". Just link to the tests or show the data here.