Have any of the rock samples (or meteors from Earth's moon or from Mars) provided a measurable amount of gold, silver, platinum or any other precious metals?
According to this 2013 paper: Prospecting for Native Metals in Lunar Polar Craters (Platts, Boucher, Gladstone) which uses spectra captured from the Lunar orbiter LCROSS, they give the measured/estimated mass abundances:
Silver Ag 0.11%
Gold Au 0.52%
Mercury Hg 0.53% (0.39% according to estimates from the orbiter LRO).
Note that this is only for polar craters which are always in the shadow. They propose electrostatic dust transport of metals which are then trapped in such cold craters, along with volatiles like water. These are small areas compared with the entire Moon, but if you consider early human resource utilization on the Moon, it might be a good place to start.
I'm shamelessly clutching the straw given by Major Stackings (who considers titanium to be a precious metal) and present the results of Mars Odyssey's survey with Gamma Ray Spectrometer (http://photojournal.jpl.nasa.gov/catalog/PIA04257)
This is the map of relative abundance of Thorium.
The truth is, any metal should be considered precious on Mars. However, in the chemical sense, precious metals are very strictly defined and neither titanium nor thorium fit the bill.