Like many words in English it does not have such a discrete meaning.

A story or experience can have a "message" the same way it might have a "moral". In fact "moral" is often defined as: the message conveyed by a story.

"Example" would have been a poorer word in its place.

Yes, a story can have a message, but "Babbage" is a person, not a story. "This story's message" has a different agent from "Jim's message". Jim is always the _author_ in the second meaning.

"Babbage's message" made the title shorter, but also misleading. A complete title of "Babbage's heart-warming" would have made it even shorter, but I hope you're not advocating in favor of that!

Reflecting today I believe Jim's inspiring message to us is to live life to the fullest even if that requires participation in extreme sports.

Jim did not write a letter. He was the "author" of the sentiment (according to the speaker) by the way he lived his life.

"Babbage's message..." and "A message from Babbage's Life...".

are not identical. The former is a personal article or note from Babbage.

I got down voted for exactly what zeteo said...

"A message from Babbage's Life..." is too long. A title can trade ambiguity for elegance if the essay is clear.

"Babbage's heart-warming message for the middle-aged"

and "A message from Babbage's life for the middle-aged"

to me both titles sound elegant but the former is misleading and the latter is correct.

The title is not trading ambiguity, it is just misleading.