However, if you read the article (either the parent or the NYTimes one) you will see that there is some thought about bringing an asteroid to one of the Lagrange points or into a Lunar orbit (something that would make the chance of it getting away and hitting Earth unlikely). In that scenario one could imagine living in one of those inflatable habitats where you worked while you operated your remote mining pick.
Getting to and from that point would probably involve a 'loan' from the mining company, which you could pay off by mining the asteroid. Of course while you lived up there you would need things like food and stuff but you could get that at the company store. And rather than actually charge you for it they will just put it on your tab. You know, you load 16 tons, and what do you get? Another day older and deeper in debt. :-)
As part of one of the lunar exploration projects I was looking at various ideas for processing lunar regolith into something more useful than just dirt. Water is pretty straight forward, basically it sublimates off stuff in a vacuum and you collect it and store it. Platinum is a different story, some sort of chemical/catalyzing process is required that does not require re-charging the chemical packs either at all or very often.