Is Surgery Necessary For An L4 Fracture With Nerve Involvement?

My sister (33F) is currently in hospital in the UK with a fractured back. This injury was incurred six days ago, after falling about 2.5 metres from a window onto a skylight. It might also be worth mentioning that she has hypothyroidism, which affects bone density. The hospital where she is currently staying wish to perform an operation, which involves installing a rod. However, my sister doesn’t wish for an operation, not without a second opinion from outside the hospital. At present, she is prepared to recover by resting her back. According to the spinal surgeon, she has fractured the lumbar bone L4, and a nerve has been compromised. Below is a photo of the imaging provided by the doctor. The doctors want to push ahead with the operation. According to them, extra pressure on the nerve could result in paralysis. However, they are also worried about the legal side of things, and respecting the patient’s wishes. Based on the imaging, and the situation described, do you think the hospital’s concerns are justified? Do you think surgery is required? And do you think a second opinion is strongly advised?