Even if we go with his story of she fell down and the stick went in her throat couldn't they still call that premeditation since he had to go back inside the house to get the knife? He had enough time to think and realize what he was going to do was wrong.
I believe that even if the stick story was true and even if he thought she was going to die soon anyway and he was just putting her out of her misery that is still considered Murder 1 because he commited an act that resulted in her death. For example if the stick story was true and he just let her die that wouldn't be murder. But the act of ending a life even if it was only a few minutes before it would have naturally makes it murder.