I'd say the title is like that (and I agree with someone else's assessment of it being clickbait-y). I think the actual article does a pretty good job in distinguishing a lot of these transforms, and honing into which one matches most.

But the title instead makes it sound (pun unintended) that what the ear does is not about frequency decomposition at all.

The fourth sentence in the article is "Vibrations travel through the fluid to the basilar membrane, which remarkably performs frequency separation", with the footnote

"We call this tonotopic organization, which is a mapping from frequency to space. This type of organization also exists in the cortex for other senses in addition to audition, such as retinotopy for vision and somatotopy for touch."

So the cochlea does frequency decomposition but not by performing a FT (https://en.wikipedia.org/wiki/Fourier_transform), but rather by a biomechanical process involving numerous sensors that are sensitive to different frequency ranges ... similar to how we have different kinds (only 3, or in birds and rare humans 4) of cones in the retina that are sensitive to different frequency ranges.

The claim that the title makes it sound like what the ear does is not about frequency decomposition at all is simply false ... that's not what it says, at all.

It's very unlike both of those, as the nice diagrams in the article explain; not only is what it is saying not obvious to you, it is apparently something you actively disbelieve.