You're Correct!

The position of your eyes at address in relation to the ball is crucial. Not only does it give you the ideal view of the line you wish to start your putt on, but also that you should be standing the correct distance away from the ball at address, assuming your weight is over the laces of your shoes and not back on your heels or forward over your toes.

This will now see you more importantly with your eyes looking down directly above your aim line.

If your eyes are not looking down on your aim line you are sure to mis-align your putter. This will lead to you missing more putts than you hole because your mind can’t correctly align you if your view is constantly changing. The next time you are on the practice putting green or even on the carpet at home try this:

Take your normal set up position, whilst maintaining your posture keep one hand on your putter and hold another ball directly under your left eye (for a right handed golfer). Now let the ball fall to the floor and see where it lands. You are looking to see the ball land on top of your ball. This would see your eyes directly over the aim line and the ball in the correct position. If the ball lands inside the ball then you could be too far away or you could have your weight too far back on to your heels. Alternatively, if the ball lands outside of your ball then you could be too close or even have too much of your weight over the toes of your feet.
If your ball lands inside your aim line then you need to adjust your set up position by firstly checking were you have your weight positioned. If your weight is over the laces of your shoes then move in a little closer and drop the ball again. Keep adjusting your address position until you drop the ball directly on to the ball you are addressing. If the ball you drop lands outside your ball then first check your weight is over the laces of your shoes, then move a little further back and drop the ball again until you drop the ball on to the ball you are addressing.

If your eyes are too far behind the ball you could miss the majority of your putts to the low side of the hole due to the putter face closing too early through impact. This can also affect your distance control due to more off centre hits.

If you have your eyes are far side of the ball then you are possibly standing too close to the ball in your address position. More importantly you will pull a lot of putts because subconsciously you manipulate the putter head trying to start the ball on the line you think you now see.

With your eyes too far inside the ball then you could be taking your address position too far away from your ball. This will distort your view of your aim line and make you push many of your putts due to the fact that you are now looking away to your far side when you look at the hole/target when in your address position.