No it is not true. It is not the washing that damages the hair it is washing with the wrong shampoo, too warm water and not properly drying your hair that does more damage to it. Just like our skin the hair has different types too. Not washing your hair regularly can cause build-up of sebum in the scalp and result in lifeless hair. Similarly, if you use too many styling products they can cause build up on the scalp, which can clog the pores and result in damaged hair follicles.
It is not mandatory to shampoo every day. Just observe your scalp health and if you feel the hair is oily or too dry just wash it with right products.