To add to my post #40, I believe that the rules of the Senate are that if a Senator explicitly references the floor remarks of another Senator, the citation must be of what is in the Congressional Record. Which can be scrubbed under the “revise and extend” rules.
I had a friend who was a Senate page in the late 70s or early 80s. Before they put in the TV cameras. He said Teddy Kennedy would show up on the floor raging drunk and go off on rambling, nonsensical rants. Which were cleaned up by his staff prior to being entered into the Congressional Record.
So, technically, Reid probably isn’t lying. He just managed to have the truth changed.