it wasn't the Californian that didn't come to help.
They reviewed this in the 90's it was actually a ship called "Mount Temple"
They realised after documents from WW1 were discovered, and they used them in a revised inquest along with the position of the wreck.
In the inquest right after the sinking an experienced sailor on the Titanic who survived said the mystery ship had "masts close together"
Documents from a German sailor during WW1 described a ship as "masts very close together, Mount Temple"
Once the Titanic wreck was found, they calculated that the Californian was miles away and although could see the rockets and flares in the distance, they were not in a position to be "the mystery ship"
The captain of the Californian was an experienced navigator he knew where he was, as he had halted the ship in the ice field, meaning he had time to exactly pin point his naval position.
The Titanic however when it originally first marconied it's distress call and position continued to travel forwards with engines at speed, meaning it had travelled out of it's distress call area by the time the ship actually sunk. Don't forget it took the ship 2hours to sink, it still had it's engines on for a while till they became flooded.
The passengers onboard the mount temple, were disgusted when they disembarked and some did go to the press, they found these recollections later from the passengers of the Mount Temple who said they could hear the screams of the passengers of the Titanic. But the captain of Mount Temple refused to push through the ice field, as he felt he would personally be liable for any cost or damage to the ship.
However once the captain of the Californian had notification from his wireless operator onboard the Californian who returned in the morning to check the radio signals received realised what had happened, the Californian navigated the ice field ASAP to reach the Titanic, but the original coordinates delivered (due to the Titanic continuing with engines on for 2 hours) ment the Californian was late to the rescue.
It's a fascinating story. But the Californian was exonerated as The mystery ship in a revised inquest, 80 odd years too late for the poor captain though.