Dilemma--volunteering help

Last Saturday afternoon I was playing with my family on the beach of a British seaside resort. It became clear that an incident had occurred in the water, when the beach patrol drove very quickly onto the sands closely followed by police cars. The policemen ran straight into the water to pull a small speedboat up on to the beach. I considered joining them to see if any assistance was required, but felt slightly uncomfortable about pushing myself forward, despite being trained in the management of patients with major injuries. A couple of minutes later, two paramedics arrived in an ambulance. Everyone seemed to converge on the small speedboat and I decided to approach the scene in case assistance was required to lift the casualty. When I approached the side of the boat I saw a great deal of blood everywhere and 8 or 10 people leaning over the patient. I asked 'Can I help?' There was no reply. I looked at a woman and said 'Do you need me or do you know what you are doing?' The lady replied to me 'No, I think it's okay, there's a doctor and two paramedics.' I backed off immediately, concerned about treading on people's toes. Twenty minutes later a police helicopter arrived at the scene and the patient had still not been taken out of the boat. Ten minutes after the helicopter had arrived and the patient had still not been moved, I once again, approached the scene and spoke to a police officer. 'I am trained to lift and turn patients with potential spinal injuries. Do you think they need any assistance?' The young policewoman went off to talk to a more senior policeman nearer to the incident, however, she did not speak to the paramedics. After five minutes, I approached both policemen again, and asked if I was required. The policemen both said no and waved me away. It was a further fifteen minutes before the patient was removed on the spine board from the boat, and put into the helicopter. I remained uncomfortable for the rest of the weekend about my response. I realize I tried hard not to offend other health care professionals at the scene, but am anxious that in doing so, I jeopardized the safety of the patient. I have no idea what training the medical bystander had or whether the paramedics were pre-hospital trauma life support trained. Should I have made more effort to satisfy myself that the most appropriate people looked after the patient?