Final answer:
The nursing assistant is principally responsible for the patient's fall, with potential contributory responsibility from the nursing home due to oversight policies. The nurse could also be responsible depending on supervisory duties.
Step-by-step explanation:
The responsibility for the patient falling out of bed and breaking his hip primarily lies with the nursing assistant who left the patient unattended with the bed rails down, despite the care plan stating otherwise. The nursing home could also bear some responsibility due to institutional policies, and the overall environment which might have contributed to the lack of communication or oversight. The nurse might have some supervisory responsibility depending on the facility's delegation and oversight rules. However, the patient is typically not responsible in this scenario as they are in the care of the nursing assistant and the facility.