1) Planetary Resources is talking about getting access to 10's or 100's of times more platinum than have ever been mined in human history, or even could be extracted from the Earth's crust. "Domestic" production simply cannot scale in this way.
2) Mining platinum is not a very profitable business--it comes out of the Earth's curst in very low concentrations. Without a doubt extra-terrestrial sources will always be able to undercut "domestic" suppliers without driving prices so low.
3) No Earth-base operation would compete with a late-stage Planetary Resources, because at any point they could flood the market and drive competitors out of business. Earth-based mining firms will change their business to extract resources for which return from asteroids remains unprofitable.
2) This is why people don't 'mine' platinum. They extract it from the leftovers when they mine copper / gold etc. The important question when evaluating the response to increased supply is the cost of just that refining step not including all the costs associated with getting to that point.
3) See 2. Unless they drive down the price of copper. However, flooding the market drives down prices so rather than saying they can provide X you need to look at how much they could sell 100 tons of platinum a year for. They can also supply 100 tons of water into LEO a year but you can't look at the current 1k to 20k/lb price of water in LEO and assume that's a constant when their supplying a 100 ton's of the stuff.
But this is a case where not only did they ignore the substantive details of the press event (Diamandis and Anderson made clear the economic case was based more on in-space use of extracted resources and the birth on Earth of new industrial techniques using once-scarce platinum group metals, and Lewicki explained in sufficient detail how they would achieve order-of-magnitude cost adjustments compared with the NASA model), but they also made truly juvenile mistakes in their economic analysis:
About $4 billion per year is spent on platinum for industrial uses. So if you're sitting on a mountain of platinum you can hope for $4bn/yr revenue for a larger amount of platinum at lower cost (given that's how much industry is willing to spend on the metal), or realistically a value lower or higher based on the the expected demand response to price. Platinum is primarily used in the auto industry, jewelry, and electronics. General motors is not going to sell more product because catalytic converters cost a few hundred dollars less, but jewelers might and the electronics industry certainly would. Either way, approx $4 billion per annum is nothing to sneeze at, and only one part of their revenue model.
This is an industry I know a lot about, which makes me wonder how accurate their journalism is in other areas where I usually just take their word...