When Heroic Acts Go Wrong

What happens when a heroic act goes wrong? Is the person who attempted the act still a hero?

I am reading a book called Deep Survival: Who Lives, Who Dies, and Why by Laurence Gonzales. Per the title, he is examining various accidents and survival situations--both those that have ended positively and those that have resulted in fatalities--and trying to figure out why some people get into dangerous situations and survive them while others do not.

Above the Hogsback, the ridge where the accident occurred

One of the situations he describes is an accident on Mt. Hood that occurred in 2002. Four friends, all in their forties, had reached the summit of Mt. Hood and were descending roped together. They had chosen not to belay, which is a safer method of descending, to save time, but that meant that they had no fixed protection and that under no circumstances could the top man fall. Of course, you can see where this is going--the top man fell. Seeing their friend falling, the other three men threw themselves to the ground and dug in their ice axes, but the top man had to fall 100 ft before he was
caught by the slack line. Humans are heavy, and they accelerate quickly down mountains. By the time the first man reached the end of the rope, he was going too fast, and one by one the ice axes of the other men were wrenched out of the ground and they too began hurtling down the mountain.

Below them, there were two other climbers. The group of four knocked the first off his feet, but one of the falling men hooked his rope over the rope of the second man. This man threw himself to the ground and prepared to arrest all five climbers. They were going too fast though, and he too failed to arrest the fall, joining them in their descent.

Stopping five falling men from hurtling into a crevasse would be a heroic act, and the man who had stopped them would be a hero, but what about the man who tried to do so and failed? Afterwards, the man who had attempted it said that he had never considered cutting his rope so that he wouldn't be pulled down because he was loyal to his fellow climbers, and that is undoubtedly a heroic sentiment.
But his decision not to cut the rope--while made in a split-second--was somewhat foolish. Obviously, he did not really have time to think, but it is clear from a common sense standpoint that a group of 5 men that has been falling down a mountain will have too much energy for one man to stop all five with an ice ax. So is he a hero even though his attempt to help was, to an outside, clearly useless? Which brings us to another question: are you a hero if your intentions are heroic? Is that enough? He ended up being another casualty of the accident, but he did his best to stop the damage. Personally, I think it is a difficult question, but overall I  think that though what he did was heroic, I would not call him a hero because he did not end up helping the situation. Other opinions?