Update:
After reading this whole thread, I went and inspected my car more closely. I believe it is my right front tire rubbing on the fender liner. What is strange (and the reason I didn't suspect it) is that I replaced my tires with RE11's in stock size 3000 miles ago and was worried about rubbing. I did a lot of low speed turns and didn't hear a thing when the tires were new. I turned the tires to full lock both ways and saw no contact. Now, 3000 miles later one of them rubs. Perhaps I should have my alignment checked. Maybe the fender liner is just sagging from material fatigue?
Now that I am paying closer attention, I have noticed that the sound starts about 3/4 of the way to full lock, and then goes away by the time I get to full lock. At full lock, the corner of the tire has moved beyond the point of contact.
Moral of story: Check fender liner clearance if you hear any rubbing or grinding sounds on this car!