You're Correct!

In your putting set up, having a good grip is essential if you are to have any chance of constantly putting well and holing more putts within 8-10 feet.

There are over a half a dozen ways in which you can hold your putter, but no matter the type of grip, you must make sure that you position your hands on the handle in a way that keeps the putter face in a neutral position throughout your stroke. If you dont, whether you use a conventional grip or a claw grip, you will find it difficult to reach any level of consistency.

To reach a good level of consistency, you will need to have some of the characteristics that are common among good putters, which include among other things:

Handle in the lifelines

It is important that no matter which grip you feel the most comfortable with, you have the handle running through the lifeline in the palm of your hands and not your fingers. This is to ensure that your wrists stay firm during your putting stroke. If you use a non-conventional grip like the claw, then make sure the hand that has full contact on the handle is holding it in the lifeline.

Back of lead hand faces the target

Having the back of your lead hand facing your target will discourage the hand from over rotating. This will help improve the starting direction of your putt by keeping the face in a more neutral position through your putting stroke.

Dont squeeze too tight

Although the amount of pressure applied will vary slightly between each individual, the best putters in the game all hold their putters fairly lightly so they can feel the flow of the putter through the fingers. This enables them to develop a fantastic touch on the greens that allows them to control the speed and distance of their putts.

Because there are over half a dozen ways to grip your putter, this doesnt mean that having a good grip is not important. Whatever way you decide to grip the putter, there is a way to place your hands that will keep the putter face in a neutral position throughout your stroke. This will enable you to hit more of your putts on your intended line and hole more putts.

To consistently control the putter face throughout your stroke and start your putt on the line you have chosen, the way you hold the putter is very important. Whether your putt is from two feet or 30 feet, keeping the face of your putter neutral to the path of your stroke is the only way to become a consistent putter.

Although the positioning of your arms can be important, keeping them straight is not essential as they will be in different positions depending on the type of grip you adopt.

Even with a conventional grip and standard length of putter, you would be looking to have your elbows slightly flexed to avoid any tension creeping into your stroke.