the phrasing implies that what they actually want is not a belly-
scratcher, as in a lazy dullard who sits back and scratches their belly with a vacant expression on their face
conversely one is not drawn to make any conclusions about the type of person who has an itchy belly, it is hardly a character flaw
and to use itch as a synonym for scratch is a travesty of the highest order, i.e. "I been itching my itch all day," "don't itch it Ricky you'll make it worse"
