Sam most certainly DID put on the One Ring. He put it on when he decided to go forward after Frodo fell to Shelob's sting at Cirith Ungol. "He simply found himself drawing out the chain and taking the Ring in his hand. The head of the orc-company appeared in the Cleft right before him. Then he put it on. The world changed, and a single moment of time was filled with an hour of thought. At once he was aware that hearing was sharpened while sight was dimmed, but otherwise than in Shelob’s lair. All things about him now were not dark but vague; while he himself was there in a grey hazy world, alone, like a small black solid rock, and the Ring, weighing down his left hand, was like an orb of hot gold. He did not feel invisible at all, but horribly and uniquely visible; and he knew that somewhere an Eye was searching for him."