"Curtain rods"...what happened to the curtain rods. If Oswald claimed he had curtain rods in the bag, where they ever found. Obviously not. Because it was a lie to cover up the fact that the bag contained the MC. And he carried it cupped low in his hand in close contact with his body. Entirely consistent with carrying a rifle.
Obviously taking the MC into the TSBD does not prove Oswald was the shooter but Oswald owned an MC, he carried a long paper bag containing an item that could have feasible been an MC. The MC Oswald owned was later found on the 6th floor of the TSBD.
This is not Sherlock Holmes territory. Obviously not every single statement in any murder case can be 100% verified. This is one of those that are 95% factual. Way beyond reasonable doubt.