I agree. There would be some unrest if the population learned about the situation. Especially, after papa Hadelio intervened and activated Yuti. The students of Helios are completely taken with the BM - they owe him enough! They won't keep quiet about the situation and the blackmailing of Blackie.
But taking the immense arrogance of the tower into consideration, I don't think it above them to take the risk. I mean, they intended to tell the prince everything about their actions which risked the lives of the heirs from the beginning. If they succeed in portraying the students and teachers as suffering from the shock the "accident" with the summoning gate and the attack of the Association caused, there will be a clash of credibility. The tower against some children and teachers. Guess whose position will probably get higher credit?
As you say, if Meredith possessed this ability it would make everything a lot easier, but there are ways for the tower to - at least try - to get out of this unscathed even without it. They already declared the BM rogue and undermined his reputation. If they now conveniently blame the Association and the BM, who is already in trouble, for the events, and declare that they probably caused the summon of such a powerful demon, they can claim that the studentss were too shocked and unable to understand the situation. Their testimonies would be made a misunderstanding. They were unable to grasp all the occurences and lacked knowledge. And the missing student Rood Crishi? Well, he was the arrested criminal who infiltrated Helios and is responsible for all the horrible events there and in Ishuella. Such a young magician with such immense power, proven to be a criminal needs to be kept in check. And who else could fulfill such a task if not the tower? The master of Opion clearly failed to control him.
See, everything is neatly explained and the public would calm down after some time. Even the nobles because it is a pain to offend the tower and they could lose some of their power/influence. The tower could even gain something from ending the danger to the public. ^_^°