Yeah Walt, there is some doubt.
When Truly goes up to tell Fritz Oswald is missing he finds him near the elevator on the 6th floor which suggests the rifle has already been found. this is the best part of an hour after the assassination.
Somewhere in all the testimonies there is a detail that nails how soon Truly has decided to throw Oswald under the bus but I can't find it...yet.
The rifle was found by Deputy Boone a Seymour Weitzman, at 1:22 where it had been carefully hidden beneath a pallet of books,
Simply because Fritz was near the elevator does not necessarily indicate that the rifle had been found at the time that Truly lied to Fritz and told him that Lee Harvey Oswald was the only man missing. We simply don't know WHEN Roy truly sicked the rabid dogs on Lee Oswald.....
I recall that some researcher studied this aspect very carefully and was able to determine that Truly chased down Captain Fitz and reported Lee missing immediately after Fritz's arrival at the TSBD.....
I'll see if I can find that researcher's name......