This is a myth!
The truth is, root regrowth actually depends upon an abundance of tree branches and leaves, so pruning before/during trans-planting is not recommended, as it will hinder root development. There is a co-dependent relationship between tree branches and roots - both must share resources to keep the tree alive and healthy, and both are reliant on each other for growth regulation. Leaves are photosynthesizers. They use water and nutrients, which are absorbed by the roots, to convert light energy into chemical energy. Leaves produce carbohydrates and sugars (energy) that are then transported and stored in other areas of the tree. Roots convert this stored energy to stimulate regrowth of the root system.
When carbohydrates are not available due to the lack of leaves and branches on a tree, root growth and transplant recovery will slow. This is why it is imperative to minimize the removal of branches during transplanting.