Yes, because Gold is not rare everywhere, just in the Earth's crust because of gravity differentiation (Gold sinks--there's probably quite a bit of it in the mantle/core).

There are individual asteroids out there with more platinum-group elements than has been extracted from the Earth in all of human history.

Yes. 433 Eros is estimated to contain something on the order of $100 trillion worth, with similar amounts of other valuable elements.

There is some evidence that most of the precious metal deposits on earth came from collisions with such asteroids.

I've done quite a bit of looking around re: 433 Eros's composition. I have found very little to suggest to me that there's large amounts of valuable minerals there. Can you cite someone that's done a composition extimate? This: http://www.psrd.hawaii.edu/Feb02/eros.html suggests such estimates are spotty at best, since the formation of the object hasn't even fully been agreed upon.

I'd welcome the evidence about precious metals coming from collisions, that meshes with some of my understanding of the early solar system, but would be glad to know more.

Does that estimate take into account the way such vast amounts affect the price curve? I would think that the gold price will fall if it is available in abundance.