The proof that this revolver is factory engraved would be a letter stating this to be the case. Of course, if you have a letter that states the engraving is factory work, it also would state the model and the caliber.
Which leads me to believe you don't have a factory letter in hand, and so to get one, you would need the caliber and model to order one.
And so I would order one. I encourage anyone who wants to know more about their particular Smith & Wesson revolver to do so.
However, having said that, my guess is the letter would not mention the engraving as the work, although attractive, does not look like typical factory engraving from that era.