I wonder if this has to do with if you attacked the knights in the Forge Knight Riot. I remember attacking some of the knights that were getting attacked, but completed the quest no problem. Wonder if it considers you "aggroing" the knights and then doesn't let you get their invite to the trial.
Yeah, I accidentally aggroed some of the knights too during that quest and I have this problem. The leader of the Crucible Knights gave me permission to attend the hearings but there is no option to tell this to Lady Webb. Also, the burned bridges option was there before and after talking to the Crucible Knights leader.