I disagree. If he had stayed with her and determinedly tried to help her get out intact until finally realizing that nothing was going to work and he was running out of time and couldn't dawdle any longer, and then helped her break her wrist carefully and as painlessly as possible, that would have been painfully sweet and heartwarming/heartbreaking.

Also, if he had offered to help her and River had instead thrown him out insisting she could do it herself, that would also have been a good route to take.