It does seem inconsistent that Oswald would shout to send up an elevator and then when one arrives, Oswald elects not to ride down on it with Givens.
"Inconsistent" doesn't really do it justice.
In reality Oswald was on the 5th floor when the elevator race was taking place. He called out to Givens to allow him onto the east elevator (Givens was on the east elevator - Williams, Lovelady and Arce on the west). Givens refused to stop, presumably because the race was under way, so Oswald called out to them to close the gate and send the elevator back up to him. Oswald was trying to get down to the first floor. If Givens would've stopped and let him on, he would have travelled down to the first floor there and then.
Even though the four men ignored Oswald, he still made his way down to the first floor because we have Eddie Piper's testimony placing him down there around 12 noon. Oswald wanted to get down to the first floor so he went down there.
The fabricated account put in Givens' mouth completely reverses this. Instead of refusing him to get on the elevator, Givens now invites Oswald to get on to travel down to the first floor. Instead of wanting to go down to the first floor, Oswald now refuses and wants to stay put. As an added extra, the Givens Fabrication puts Oswald near the southeast corner of the 6th floor, the scene of the shooting. In this invented scenario Oswald now had the time he needed to organise the Sniper's Perch and assemble his rifle.
In reality he never had this time. Bonnie Ray Williams was up on the 6th, probably before 12 noon. The workers broke for lunch around 11:50am. All Bonnie Ray had to do was wash up, collect his lunch, buy a bottle of Dr Pepper and return to the 6th floor. I doubt this took more than five minutes to do.
There is no time for Oswald to make his preparations if he was down on the first floor while Bonnie Ray was on the 6th.
Another 'lie by omission' committed by the WC Sham was Arnold Rowland's observation of a white, slender man carrying a scoped rifle at the southwest end of the 6th floor. This stunning piece of evidence was simply ignored by the WC, as if Rowland had made up this observation and, by some miracle, had guessed there was a white, slender male carrying a scoped rifle on the 6th floor of the TSBD building.
And the gullible Nutters just swallow down everything they are told to, ignoring the string of obvious lies and manipulations that prop up their spoon-fed beliefs.