For the G chord I wouldn't put my thumb that low. I actually keep mine over the top of the neck. More comfortable for me that way. If your ring finger can touch the G string that tells me you might not be on the very tip of your finger. You want your fingers to be almost on the very extreme tip when touching the strings. If you touch the string with more of the "meaty" part, like the pads of your fingertips, there is more of a chance that your finger will take up extra room and hit the upper strings.

Here are a few pictures I found. Notice how they all have the same angle, have the thumb over the neck, and actually the ring finger isn't even all the way to the fret. For that chord that just isn't practical. It can be a little back or to the middle, but never fret at the very back.

http://image.shutterstock.com/display_pic_with_logo/8438/8438,1119830589,1/stock-photo-a-hand-taking-a-guitar-chord-g-major-390501.jpg
http://www.learnhowtoplayguitarforbeginners.com/images/gmaj.jpg
http://www.gear-vault.com/wp-content/uploads/2010/02/g-major-chord-guitar-lessons.jpg