So, when a hand reaches in to pull Frodo out, it's easy to think it would be Sam's. However, it was Gollum. Frodo was visibly shocked at what he'd seen, and perhaps at Gollum saving him.

He continued to use his invisibility to catch fish more easily with his bare hands. As Sméagol transformed into Gollum, he grew averse to warmth and light, so he dwelled in the caves of the Misty ...