Going by the DS post, there would have been NO way anyone could have manipulated the screens, the IBA/ITC would have had a fit and ITV would have entered second scandal like to the one from the 50s/60s. I think that alone would have lost Thames is franchise., maybe not straight away but at the next round...
I don't believe ITV itself was affected by the Twenty One scandal. The original format was heavily tainted in the US but by the time that came out the show had ended over here anyway. Twenty One was effectively dramatised from head to foot and the entire charade in that show was scripted, the reactions, the questions, the outcome, the entire saga was planned. It affected the entire quiz show format both in America and over here when the truth came out.
Of course on the issue of integrity of Strike It Lucky, its probably more than the job of the producer, and Thames as a whole, was worth to blatantly fix the show. It would have been common practice to tip the balance in the favour of the show, otherwise everything would get given away and cost Central/Thames/LWT or whoever a fortune and you wouldn't tune in to see if Fred and Daphne are going to win the car on Bullseye this week. But that's different from "fixing".
I suppose there were any suspicions the IBA would have said something to Thames at the time. Maybe they did, maybe they didn't. It may have been all above board and totally random. After all if the regulator of the time, which was far more hands on than anything that's replaced it since, wasn't happy the show wouldn't have stayed on the air in that form surely?