OK, so to unpack this, it's going to take a little bit of work. Hang on one...
First, you're making several points and asking several questions here.
Maybe they do and maybe they do not. I have no doubt you've encountered that attitude, but I am not as sure that the people who exude this sense of confidence are really all that convinced of their own abilities. In general, I have found that most people are a rather huge pile of insecurities about nearly everything. It's only a few sorts of people who are ACTUALLY as confident as they claim to be, and yes, that type of confidence can be wholly or partially without basis in reality.
Again, maybe he thinks that and maybe he just says it. However, having experienced a bit of being young and a bit of being older, I can say that it seems to me that it's very natural to think of oneself not as the guy one sees in the mirror, but as the guy one sees through the lens of time, which is to say 'back in the day' but also a tad bit buffed up beyond what reality might have actually been.
And why should they not? Would it be more seemly if they sat in their chairs and thought poorly of themselves?
Yes, I believe that's fairly common. I don't see it as being of any particular consequence, however. To put it bluntly, so what?
I have been to Las Vegas. I have gambled in Las Vegas. I did not leave a winner. But talk to anyone - they all left
'breaking even' at worst. No one likes to say they lost a bundle there. Yet, statistically, most have to have lost and lost big. Does it matter, though? Really?
Why do people think of themselves as good drivers, good cooks, good lovers, able to handle huge amounts of booze without effect, and so on and so forth? I guess because it's part of the human condition. We see ourselves as capable, caring, intelligent, strong, handsome, etc, against the backdrop of a world that mostly doesn't really care much whether we even exist. Why would we want to see ourselves as sniveling cowards, useless and selfish mewling little oxygen thieves, even if that's what we really are? We see movies and read books about heroes who rise to the challenge, handsome men who get the babes (or vice-versa or what-have-you), things which explode and fights where good guys win, and we're sitting in our armchairs and mostly doing nothing and as Pink Floyd put it,
"one day you find, ten years have got behind you, no one told you when to run, you missed the starting gun."
So maybe we exaggerate a bit here and there. Maybe in our memories we were a bit faster, stronger, more capable in all ways, and in our mind's eye, we're still that person. Older, slower, fatter, but still able to put that aside if the moment calls for it... Truthful? Probably not, but we make movies about it.
And finally...
I think the answer to that depends a lot on what you think you need to prove and to whom. I would guess there are quite a few things I imagine myself capable of doing which I cannot. But I also know that I've faced the abyss a time or two. I've come up lacking in some ways, and capable in others. You never know what's around the next corner. About all you can do is keep training and keep your head on a swivel. You will either have a great story, a new set of scars, or it won't matter anymore. And so it goes.