It is not so black and white. One might (and normal person should) feel a stress reaction with rising levels adrenaline and suchlike in his bloodstream, and it is normal, it might even be beneficial, if one was trained to benefit from this mind state. I become more resolute from this, more concentrated than usual, sometimes even more concentrated than it is good for me because I might miss some important detail.
> If a tyre blows out, most of us wouldn't scream and close our eyes, we would try and steer to safety.
I never was in this situation with a blown tyre, but I was in some other situations when there was a danger to my life (or I believed that it was) I become extremely concentrated, almost silent (except for occasional curses), but when I needed to communicate, I did it loudly and with a good deal of swearing. I think that communication for me in these situations is like a distracting hindrance, so if I need to do it, I'll do it in a way that will make it unnecessary to repeat it.
The communication of the pilot have not a hint of his emotions. My mind was blown not because of his perfect actions (I expect perfect actions from a professional), not even because the lack of swearing. It is the tone of his voice, it is completely composed, almost relaxed. I can imagine myself in this situation restraining from shouting and from swearing, but my emotional tension would leak through my voice, I wouldn't even try to hide it.