Bleeding from sun-baked lips and weeping, they told of the night the mountain took six of their friends in blizzards that left no trace of disaster except an unidentified body, and Ms Hargreaves's boots, jacket, and harness.
As they did so, a Pakistani army officer disclosed that he had begged Ms Hargreaves not to make her assault on the mountain, warning her that because of the weather conditions, to do so would be "suicide". Ms Hargreaves was missing her husband and children greatly, and had appeared to relent, Captain Fawad Khan said, but then her passion "gripped her again" and she set out on her last climb.
Lorenzo Ortas, 42, and Pepe Garces, 38, were airlifted to Skardu in the Karakoram range of the Himalayas after six nights on K2 with neither tents nor sleeping- bags. They confirmed that Ms Hargreaves had fulfilled her dream of reaching the summit of K2, but they also described the mountain's terrible revenge.
Mr Ortas said he and Mr Garces survived only because they were too exhausted to make an assault on the 8,610m peak last Sunday. Instead, they stayed at Camp 4 at 8,000m while Ms Hargreaves, 33, the American Rob Slater, New Zealander Bruce Grant and Spaniards Lorenzo Ortiz, Javier Escartin and Javier Olivar struck out for the top.
"We spoke on the radio and they said they made the summit between 6 and 7pm," Mr Ortas said. "But then, between 8 and 10pm, many winds came. It was very, very bad. Our tent broke and then flew away, and we lost our sleeping-bags.
"I think some of the people decided to stay next to the summit, but I also think Alison tried to come down. But the wind was very, very high, and I think she will have been blown away."
The surviving Spaniards lay in the snow until early morning and then tried to make it down the mountain. Before reaching Camp 3 - normally an eight-hour march, which took the exhausted men 50 hours - Mr Ortas said he saw a jacket, a pair of boots and a harness, all belonging to Ms Hargreaves.
"Her jacket was purple with flowers on it - there was only one like that. It was Alison's. She is on the mountain. She is dead," he said.
Of the other climbers, he said, there was no trace.
"At Camp 3 we could see a body which I think was Alison's," Mr Ortas said. "But it was 300m away. It was dark, and I was too exhausted to go and look at it. I feel very sad now and I just want to go home. They are all dead."
It is understood that the Pakistani authorities, who interviewed the Spanish survivors last night, have taken their description as formal confirmation of Ms Hargreaves's death.
As the men made emotional phone calls home, three British climbers described the earlier accident in which Paul Munn, 52, the president of the British Mountaineering Council, and his fellow-climber Geoff Tier, 51, died.
They had been climbing Haramosh 2, a 6,665m peak 40km from K2, on 6 August when disaster struck. Their friends, Brian Davison, 33, Dave Wilkinson, 49, and Colin Wells, 33, had successfully made the first-ever ascent of the peak when a huge sheet of ice crashed down on Nunn and Tier.
"We were at camp making tea, and the other guys had made the summit and were on their way down," Mr Davison said. "They were only 300 metres away and we could hear their voices when suddenly we heard the crashing of an avalanche. We ran to help, but they were buried under blocks of ice as big as motor cars. We had walked under the ice earlier and we were OK. If they had passed it five mnutes earlier or later they would have been all right too. It was just tragic bad luck."
Whereas the Haramosh II deaths can be attributed to bad luck, there is growing opinion in climbing circles that Ms Hargreaves' death was caused by tragic folly.
Captain Fawad Khan, the liaison officer between Ms Hargreaves' team and the army rescue services, said yesterday that he had begged Ms Hargreaves not to make her assault on K2, warning her that to climb would be "suicide".
He said he pleaded with her not to leave base camp as the weather on the peak deteriorated - but she ignored him
"It was suicidal and I told her so," he said. "She had already tried twice and came down to base camp. There was a big conference there, where most of the other climbers decided not to return. There had been snow for the 10 previous days, and it was lying 2ft thick at base camp and 2m thick at Camp 4.
"I said to her : 'If you go back up, you will kill yourself, because at Camp 2 you have already been unable to find your ropes and tents and equipment under the snow.'"
Capt Fawad said Ms Hargreaves appeared to concede, and asked him to arrange porters. "She was all ready to leave when suddenly she said : 'I will climb.' I was very surprised. I thought she was crazy," he said.
"There were times when I thought she would give up, not because of the mountain, but just because she said she missed her children and husband so much. But then the passion seemed to grip her again, and she said she would climb on.
"She never said that this would have been her last climb," the officer said. "In fact, she said she would be back."