Yes, it is right to view the pilot, CB Sullenberger, as a hero for the mental composure and technical skill he showed after he (reportedly) lost power in both engines.* Plus to celebrate the combination of luck and teamwork by aircrew and rescuers that allowed everyone aboard to get out of the airplane alive.
During my days of amateur piloting, I was always amazed by the rigor and discipline of professional airline crews. Every two years, those of us in the amateur business were required to go through Biennial Flight Reviews in which you'd fly with an instructor who would simulate various problems to see how you'd react. ("OK, you've just lost power, tell me where you're going to land." Or, when you're ten feet above the ground preparing to land, "A deer just stepped onto the runway - GO AROUND [abort the landing] now!") Many amateur fliers choose to get, or are required by insurance companies to get, "recurrent training" every six or twelve months.
But airline crews are drilled and tested and measured again and again and again, without letup, throughout their working careers. In their full-motion simulators, they're trained to respond to every disaster, and combination of disasters, that might possibly befall an airliner. Loss of power just as the airplane is taking off. Engine fire at low altitude. (Contrary to general assumption, problems at low altitudes are usually more dangerous than ones high altitude, since you have less time to deal with them before the airplane hits the ground.) Hydraulic failure along with the fire. Plus, being in the middle of a thunderstorm. And so on.
Some professional pilots are "smart" in the normal sense; some are not. Some are likable and admirable; some are bores or boors. But all of them are made to develop and maintain reflex-like responses to these emergencies. They are also forced to think through the decisions they would make if faced by disasters they will probably never encounter through their whole flying careers.
Why is riding a commercial airliner in the US statistically about the safest way you can spend your time? Partly it's because of the advanced, powerful, and multiply-redundant nature of the machinery, and because of the regulatory standards to which it's held. But the airlines' extraordinarily safe record also says something about the skill, responsibility, and judgment of (most) people flying the craft. As it happens, nearly all flights are routine, and it becomes tempting to think of their crews as glorified bus drivers. But they're conditioned to think, at every stage of every flight, What would I do if XXX went wrong, right now?
And birds? Birds are a much more serious worry for people flying airplanes than you would think, no matter the size of the plane. Obviously it's bad for the bird when it hits a hard metal or composite structure at hundreds of miles an hour. But it's surprisingly bad for the plane too. This detail in a recent NYT story rang true to me: "The impact of a 12 pound bird hitting a plane traveling at 150 miles per hour is equal to that of a 1,000 pound weight dropped from a height of 10 feet, according to experts on bird strikes."