I took typing classes, and they taught that the 6/Y/H/N are typed by the right hand (and 5/T/G/B by the left) as you say, but I have been programming for 16+ years and have gotten into the habit of typing 7/Y/H/B with my right and 6/T/G/V with my left. It just feels more natural. I don't know why they teach it the way that I learned it. Just doesn't make sense to me.
And just for reference, I primarily use Mac computers, and all of their (modern) keyboards have the 6 key significantly closer to the left hand (about 3/4 of an inch "as the crow flies" from the F to the 6 vs the J to the 6).