Those fear chemicals (adrenaline, principally) are the body's responses to the mental perception of fear. The brain perceives (rightly or wrongly) that there is something to be afraid of, so it sends nerve impulses to various glands, which order them to release the chemicals to put the body into high gear for "fight or flight" situations.
Now it's fairly easy to fool the unaware brain into mistaking the physiological changes caused by the chemicals for the actual fear, but that's an illusion. For instance, if you've ever had allergy testing, they'll often give you a shot of adrenaline afterwards to deal with aftereffects. This produces the same physiological effects as fear - shaking, elevated heart rate, sweaty palms, &c - even though there's no cause for fear. If you weren't aware of the cause, you might think that you actually were afraid of something.
Same applies to most, if not all, of those other hormones. They're effects rather than causes, though the unaware can be fooled into mistaking effect for cause.
As someone who's been through panic disorder, I agree that there's a difference between the mental aspects of fear with the physical sensations caused by the chemicals, but it's not a strict cause/effect; rather, they form a feedback loop.
Perceiving something fearful activates the chemicals, sure, but the presence of the chemicals also cause the brain to seek out things to be afraid of. If you consciously think there
is something to be afraid of, you put out even more chemicals. If you look around and convince yourself there's nothing to be afraid of, the feedback loop breaks and the chemicals wind down.
I suppose you're right that (barring some gland disorder) the loop always starts with a mental perception, but the initial perception may be subconscious, which leaves the conscious mind casting about for an explanation of the feelings.
The majority of people would respond in a normal fashion, as MMM did, and what he describes in the article is sort of like cognitive-behavioural therapy used in counselling to combat anxiety
+1. Most people come by this skill naturally - they feel fear (the chemical) and find some explanation (whether rational or irrational, right or wrong) for why they feel that way, which allows them to break the feedback loop by getting away from their perceived cause.
If you make the mistake of thinking that the fear sensations themselves are the cause (e.g. if you think you're about to die from a heart attack because of them) then it feeds on itself and gets out of control, becoming a panic attack. Once it's happened a few times, even though you've realized by now that it's not a heart attack, it can become a habitual response, where any sensation of fear makes you afraid of having a panic attack, which of course brings on a panic attack: panic disorder.
It can take an awful lot of therapy to break that habit - it's like the difference between convincing someone who just read about investments for the first time that tax-advantaged retirement accounts are a good thing, vs. trying to convince someone who has believed for years that 401ks and IRAs are a government conspiracy to enslave the people. ;)