I think there may have been another reason the team picked up Lindley when Palmer went down. Palmer was done for the season - you had to rely on Drew Stanton if you wanted to win. Stanton was a career backup, couldn't crack the starting lineup of an 0-16 team, and had backed up 3 different #1 overall picks -- two of them as rookies. He probably wasn't exactly brimming with confidence.
Now, he is thrust into a situation where he has to lead a team with Super Bowl aspirations. That's pressure enough, he doesn't need to be looking over his shoulder. Even if Stanton was the better option, if there was a "known commodity" on the team (Grossman, Campbell, Freeman, Tebow, etc.) as soon as he started struggling, the fans and media would be calling for that option. Think of what the pressure would be after the first Seattle game and the Atlanta game. They may not have won the Chiefs and second Rams game if Stanton had that extra thing to think about. With Lindley and Thomas back there, nobody called for a QB change.
So, the choice was either to take as much pressure off their QB as possible and hope he stayed healthy, or sign a veteran in the unlikely event Stanton got hurt and potentially cause some unneeded strife. They gambled and lost.
BTW, all four QB's I mentioned, as well as almost every other option (Leftwich, for example) were former first round picks that never amounted too much. Indicative that they had trouble adjusting to the NFL game. What makes anyone think they would adjust to Arians' offense so quickly?