There are so many angles to view this from.
Yes, empathy is supposed to be natural but the degree varies between people. It's human nature or may be related to culture.
The practical side of helping someone after a fall may be conditioned by your lack of first aid training and/or realising you could do more damage. In the situation I shared, I asked the elderly gentleman if he was alright. May seem a daft question when he'd cut himself and broken his glasses. However, he managed to stand and walk to a nearby bench.
When you watch the numerous programmes about paramedics, even they are cautious about moving someone until they've ascertained there's no spinal injury at the very least. Then they are trained to a very high standard. Contracting pneumonia after a fall is common with the elderly.
On the flip side, I do recall media reports some years ago about doctors and nurses refusing to answer calls for medical assistance on flights, due to possibility of being sued.
Around 15 years ago, my late uncle was taken ill (he had lots of underlying health problems). My cousin was not happy with the hospital he was taken to and thought it contributed to his death. I very tactfully suggested that with said hospital also treating injured military personnel, he could not have gone to a better place for medical expertise.
Hopefully, those threatening to sue will take a step back and realise that there is no case. However, grief can manifest itself in so many different ways.