Fred Rogers, who hosted the show "Mister Rogers' Neighborhood," had no tattoos on his arms or elsewhere. The rumor has roots in Roger's choice to wear long sleeves while in character on his television program. It is often combined with the untrue rumor that Rogers served in the military.
Long sleeves were a purely stylistic decision on the part of Rogers. He strove to maintain formality in his interactions with children, casting himself as a teacher or parent figure rather than as a friend. In order to convey authority, Rogers always wore long sleeves and button-up shirts on the show.