The circle that appears on the pokemon when you try to catch it is only used to determine whether you get a 'nice', 'great' or 'excellent' throw. If you get the poke ball in the circle when it's large, you get a nice throw. If it hits the circle when its a medium size, you get a great throw. When it hits the circle at it's smallest, you get an excellent throw. This is where the misconception comes from, since the excellent throw gives you more exp and a greater chance of capturing the pokemon.
If you don't get the ball in the circle at all, it doesn't matter what size the circle is. Since it's EXTREMELY HARD to get an excellent throw (without the use of this trick), you're going to want to throw the ball when the circle is medium in size. A great throw is not too difficult to get, and that added EXP and capture chance will go a long way towards making you a Pokemon master.