I've had a chance to screen some things that others haven't, and while I've never seen the premiere episode, in the past year I've had a chance to view the second episode. I'll tell you for certain, the disaster isn't the second episode, although a few things jumped out to me as odd about the second episode...
It opens with a champion who has $10,500 (indicating a 21-0 win) declaring that he was "lucky" last week and announcing that he was retiring without facing another opponent. This feels a LITTLE bit like a show trying to make a fresh start on night two. Also, there are definitely a few signs of lessons from the Dan Enright School of Acting ("Let me see....I think I'll risk, uh...let's see....ten. Yes, ten points" followed by a lot of rubber-faced thinking out loud once the question is asked).
Here's the problem I'm having though. The episode of The American Experience dealing with the quiz show scandals shows a clip of a disastrous game of Twenty One that is framed in the narrative as if we're seeing episode #1. The champion who walks onstage at the start of episode #2 is NOT either of the people seen in that clip. The contestants at the END of episode #2 aren't the people in that clip either, so there's a chance that's not episode #3 either.
But then it gets even trickier. It has to do with the set of the show in that American Experience clip. It's the familiar version of the Twenty One set that we've all seen. Episode #2 has a weird, weird set. The isolation booths are enormous (a wide shot reveals that there's a camera operator physically inside each booth) and Jack has the scoreboards mounted on his lectern. It's possible, though unlikely, that they'd start the series with one version of the set, try a completely different version of the set, and then go back to the version of the set they started with.
But ALSO, we have the pilot for the show that was shot in March of 1956. The set they used for the March pilot, though not identical, is closer to the familiar version of the set than the weird giant-booth version of the set seen in episode #2. So, my two theories...
#1. They actually did switch out one set and then switched back to it early in the run, and the premiere was the disastrous game.
#2. If none of the newspaper accounts are mentioning that the game was a disaster, I think there's a real possibility that the bad game was a pilot/"shakedown show." We know that NBC shot a not-for-air episode of The Price is Right with a week to go before the premiere to work out the bugs. There also exists a Tic Tac Dough pilot that's apparently the same deal, the show had already sold and they shot a pilot right before the premiere to see how it looked. Maybe they shot a Twenty One pilot a week out from the premiere, it went badly, Geritol said "This sucks, rig it," and they decided to go ahead and try a different set once the show went on the air, hated it, and went back to the pilot set after two weeks because they hadn't junked it yet.
The thought has also crossed my mind that the clip in American Experience was a clip from the END of the run, some time in the fall of 1958. Maybe they tried to salvage things when things were looking bleak and they wanted to prove to themselves "We can do this without rigging it." I've never heard it said that they attempted that with Twenty One, but it wouldn't surprise me. I'd be fascinated to see the last month's episodes of the rigged shows to see what they looked like while drowning in bad press and office turmoil.