Woody,
I'll go even further than that--sometimes memory tests don't reveal faulty memory--simplest test is to take all the stick of memory out of your computer and replace them with other sticks, and run it for a day, two or three and see if you're still getting the freezes.
If, by swapping out the memory, the freezes go away (and I suspect they will), you can figure out what stick (or sticks) of memory were bad by carefully swapping some in and checking again. A good Genius might be able to help you with the extra sticks of RAM, or even offer to do the swap testing themselves if you can show them how to make the desktop freeze up pretty reliably.
Hope that helps,
-Brad