Scrimgeour says:
"A Snitch is not touched by bare skin before it is released, not even by the maker, who wears gloves. It carries an enchantment by which it can identify the first human to lay hands upon it, in case of a disputed capture."
"Lay hands upon it" is a bit more ambiguous than "touch" because the definition implies to manage with the hands, i.e. to have control of it. So if that reading is correct, then it will settle the disputed capture by indicating which Seeker had first control of it.