That's not even remotely true. Most things in nature people talk about being fractal aren't, in the mathematical sense, at all. They show statistical variation between areas and only have a few levels of self-similarity. A few minutes of Googling with confirm that.

You're missing the forest for the trees - perhaps literally.

Trees are a perfect example. Fractal in form, down to a certain level; but also an example of something that builds over time like a cellular automaton and is being influenced by the environment. Compromises are made, the perfect form is impossible to achieve, but the gestalt is still there.

The fact that the most realistic simulated / computer-generated trees we can render are made primarily of simple fractals is a great indicator.

We see the same thing in terms of self-similarity in mountain ranges, lightning, rivers, lungs, and now clouds and water. At this point if you want to deny it, all I can surmise is that you either never go outside, or simply don't know what to look for.

There is an important distinction you're missing between how you're using fractal and how this article is using it. It's saying something fundamentally different, though related, about turbulence, than you're saying about trees etc., even if you don't realize it.

I live in the mountains and I'm outside in a forest setting multiple times a week. I see exactly what you're talking about; it's just not the same as what the article is saying, even if you use the same word to describe it.