I didn't really understand her comment with regards to the call, was she "claiming" to call the drivers family or the casualties family? Theres no way it would be the latter, i think most people know that wouldn't happen that job is down to specialist liason and would not be done over the phone. Ever.
However if they had taken the driver of the vehicle involved into their car during this time there is a possibility he or her on the drivers behalf rang someone to say hes been involved in an accident, shock does wierd things to people he could have rang his wife and said "I've just killed someone" however i find it unlikely you as a passerby say that " Hi im just sat with uour husband, he's been involved in accident and killed someone, but your husband is ok "?
However that contradicts the rest of the story that she was with the casualty throughout.
I think the event happened however the finer details are massively embellished.
They most likely were on scene at an RTA, Josh as a PC will have some first aid training and likely he would of attended the casualty, bear in mind most of the police only actually have quite basic first aid training despite their role her involvement would likely of gone no further than offering tlc to the driver until he was questioned by the police. She may or may not have been witness to the procedures that followed.
As the saying goes don't let the truth get in the way of a good story.