God hears children's prayers better?

In the midst of a tragic story in the New York Times of a soldier who lost both his arms and his legs comes this quote from his mother:

“That was one of the worst experiences of my life without a doubt,” she said. “I went back to my room and called one of my best friends, whose son is a youth minister, to get the children to pray. God hears children’s prayers better. I said, ‘Get the prayer chain going. I’m losing him. I’m losing him.’

“If I hadn’t been there,” she added, “I feel I would have lost him.”

I feel great sympathy for this woman and the pain she was going through, and given her experience I certainly give her a lot of leeway to express her pain in ways that may not make sense to me. But at the same time I also think it is really sad to hear anyone say something like that. It does make me wonder if there is a common belief out that that somehow "God hears children's prayers better," or that the only thing standing between someone living an dying is a loved one who prays hard enough or who enlists an army of children to pray on their behalf. And what does that say to the people whose loved ones don't pull through? Are we supposed to tell them that they didn't pray hard enough or make use of their local youth minister that the death of their loved one is somehow their fault?