Pointing out that Ayn Rand didn't really understand the capitalist system she eulogised is far from a mere "nitpick". You seem to have missed the entire point of the criticism:
zillionaires devoting time that could have been spent more productively to giving people lifts is exactly the kind of "charity" Rand is trying to pretend it isn't.
And when the heroes do help each other, just in case you think they might be supposed to be doing it out of a sense of kinship, Rand tends to have them say things like this:
"I hope you know it's not for your sake that I wanted to help you fight."
He smiled; it was a faint, friendly smile. "I know," he said.
"It's not out of pity or charity or any ugly reason like that. Look, I intended to give you the battle of your life, down there in Colorado. I intended to cut into your business and squeeze you to the wall and drive you out, if necessary"
He chuckled faintly; it was appreciation. "You would have made a pretty good try at it, too," he said.
"Only I didn't think it would be necessary. I thought there was enough room there for both of us."
"Yes," he said. "There was."
"Still, if I found that there wasn't, I would have fought you, and if I could make my road better than yours, I'd have broken you and not given a damn about what happened to you"
As with all religious texts, Atlas Shrugged produces its blind devotees who will assert literally anything to avoid confrontation with any other aspects that might conflict with their worldview. But it's a curiously selective reading of the text that argues a book whose key moral messages include the slogan "I will never live for the sake of another man, nor ask another man to live for mine" is about a personal system of individuals helping each other, and not the negation of said system in favour of the logic of self-interest and cold hard cost-benefit analysis.