They have both taken inspiration from the original story "The Final Problem" where Holmes fakes his death:
Holmes and Moriarty are engaged in a battle of wits which results with most of M's gang being arrested by M himself escaping to the continent (where Holmes and Watson are).
Whilst Holmes and Watson are taking a holiday they go for a walk to the Reichenbach Falls but Watson receives a note saying that there is a sick lady back at hotel so he returns.
This is a ruse by Holmes to ensure that he faces Moriarty alone (as he does both the series and the film).
They fight at the top of a cliff (in the series a building, the film a ledge) next to a lethal drop.
Watson rushes back to help Holmes but is too late and finds a note which Moriarty allowed him to write apologising for deceiving Watson. There are footprints leading to the edge of a cliff and signs of a struggle but no returning foot prints. They are presumed to have both fallen to their deaths.
We find out in 'The Empty House' that this was a ruse by Holmes (after spotting Sebastian Moran) to flush out the remaining associates of Moriarty.
- Holmes faked his own death
- Watson was kind of a witness (the note is switched to an eye witness)
- The age is just reflective of how the direction imagined the character and they both would have read this book.
Doyle wanted to kill off Holmes, the creation of Moriarty was designed to give him a climactic send off. However, Doyle's desperation for money and the public outcry forced him to bring Holmes back to life again.