The story of the Czar's Parker is well cataloged and a completely different deal from this one. Your story needs provenance, without that it's just a story and adds absolutely no value to the gun.
I've got a friend who has a single 4 gauge shotgun that all evidence points toward being originally owned by Teddy Roosevelt but he's got absolutely no hardcore provenance hence it's just a nice gun.
Another friend has a shotgun that he knows for a fact was owned by a famous gangster but there's absolutely no hard provenance hence it's just a beat up pump gun.
Your sounds like a nice one and would stand on it's own merits as to value, your story of it being a gift from Roosevelt is simply a story. Find a photo of him handing the gun over, a letter that talks about the gift, records of the guns sale to him, or something to that affect and you might have some addition to value. Till something like that turns up it's just a nice Parker shotgun that's probably got some value.
Destry