What really is 人身事故【じんしんじこ】 (jinshin-jiko) we often hear at train stations? Some say that it always means that somebody just threw him/herself onto a train track and got killed. Others say that it's just any kind of train accident that involves humans; it doesn't necessarily means somebody lost him/her life in it.
It is technically any "accident causing injury or death" however as your question points out it is generally accepted in society that it means that there was a fatal injury. In the event that this is displayed on the monitors it means that the train company had to stop train service (or later service is delayed) to deal with the accident.
Anecdotal: A friend of mine slipped in the gap between the train and the platforms and train service was temporarily suspended as a 人身事故
The latter is correct.
When an accident happens, the train company need to stop trains and to let passengers know what is going on right away. Then don't know why the accident happened yet. Technically speaking, it is police that investigate an accident and find out the reason.
Right after an accident, often it is apparent to everyone that the victim got killed, but not always.