Rand, Hurin and Loial mysteriously vanish from Igntar, Perrin, Mat and the rest of the Shienarans. The three wake up under what appears to be the same stone column in a slightly different world. Cut off from the rest, the three begin to figure out where they are and how to get back.
"... You'll get us back. And if I die, if you can't take her my body, you'll let he know, so she has that, at least." [Hurin] was no longer questioning in the end. A note of confidence had crept into his voice. ...
"I will do my best, Hurin." And because Hurin was Shienaran, [Rand] added, "by my House and honor. A shepherd's House and a shepherd's honor, but I'll make them do as well as a lord's." ...
Guilt rippled through Rand. [Hurin] thinks you'll see him home now, because Shienaran lords always keep their word. What are you going to do, Lord Rand? "None of that, Hurin. There'll be no bowing. I'm not - " Suddenly he knew he could not tell the man again that he was not a lord. All that was holding the sniffer together was his belief in a lord, and he could not take that away, not now. Not here. "No bowing," he finished awkwardly.
Hurin and Rand, The Great Hunt, p. 184-185
All the leadership training in the world doesn't really prepare anyone for the initial shock of responsibility. Until this point, Rand has been reluctant to step forward. Before, he was content to follow Moiraine and Lan; since Fal Dara, he's been planning on leaving on his own. Now, his real leadership journey begins. He's got a small team, lost in the wilderness, trying to accomplish two objectives: get back home and find Mat's dagger.
Initially, Hurin comes across as somewhat helpless in this situation. I think it's the opposite. Hurin's faith in the structure he knows immediately gives Rand a strong foundation of positional authority. Rand doesn't have to establish that he's in charge, it's freely given to him. This brings its own set of challenges, notably how to get out of the crisis without breaking Hurin's trust. This is a pivotal situation for Rand; building on his sense of duty and responsibility and establishing him as a leader.