Pat, I can see why you are confused. You were given misinformation. The purpose of a walking foot, is to allow the top and bottom layers to move at the same time. It is also refered to as an even feed foot. When sewing, the feed dogs move the fabric along at whatever pace you have set for a stitch length. In garment construction, the walking foot allows plaids and other precise fabric matching to feed thru the machine evenly.
To this same end, quilters use the walking foot for all straight line quilting, such as quilt in the ditch or putting on binding. It is necessary to use the walking foot to feed or push the top layer at the same rate the feed dogs are feeding the bottom layer. Without this tool, the fabric and batting would be dragged a bit by the pressure of a stationary foot. This it not a problem in sewing two layers of cotton fabric in piecing, so I use a quarter inch foot.
For free motion quilting, there is another foot, called the darning foot also refered to as a free motion foot. It has a spring in it to allow it to hop at the same rate the needle moves. It's only purpose is to apply even pressure as the needle exits the fabric. Your hands control the movement of the quilt. Once you understand the mechanics, you will see each purpose as an aid in successful quilting. Sure hope this helps. :D