OP: What are ya? A lawyer or sumthin?
Just kidding.
While what you say make sense, matching a serial numbered gun to the letter does "Authenticate" that that serial numbered gun came from the S&W factory in certain fashion, where it began it's journey and when. But it does not do much more. History of ownership would require other documents. Post manufacturing modifications would require yet another set of documents (IE Lew Horton).
I guess to me it Authenticates that S&W built the gun and when & where it became a used gun.