I'm curious about how they plan to bring these materials here. I assume changing the trajectory of the asteroid towards Earth wouldn't be a very good idea, considering the potential risk of impact. Maybe small chunks of material brought by numerous cheap reentry capsules are the way to go.
I'd crash them into the moon (no atmosphere, so they wouldn't burn up on entry) for about a decade, then send ore-processing robots to smelt them down, then figure out later how to bring the results back.
Good idea at first look, but it would be tricky to get the trajectory right, though. The Moon's sphere of influence is tiny compared to the Earth's. You would need a guidance package and, perhaps more importantly in terms of cost, onboard rockets to change delta-v (and only one-use because they would be destroyed on impact).
