Annnnd

I was thinking the same... Also the knights should apologise too

I think it was very fair that she apologized. Just because he really happened to be a criminal, doesnt gave the mage tower the right to conduct themselves how they have done their investigation. They didnt care if he was truly innocent or guilty, they used that as a excuse to scrutunize them, regarding facts. They basically stormed and ambuished them on a scribbled text, with vibes and feelings and no evidence. And that all happened while FL was in charge, she reprimanded them halfheartedly and brushed that off, because of also her own bias. I think she was more far more wrong, than he was. He was only bewildered and acted on the surprise, which wasnt right but wasnt really wrong.

Actually it gives the mage tower the right even if he was innocent because that's the kingdom's law. All suspected to be even related to black magic, not really using it, must be investigated by the mage's tower and they have full juridiction. Arasila did everything by the book and explained that to them. She also reprimended the mage who was disreapectful on the spot.

No, the investigation was valid, not how they handled it. ML even states that he could have filed complaints for wrong conduction.
Plus FL did not give a shit about how her subordiants conducted themselves. They were running wild harrassing the knights, without her knowledge maybe, but also she did not supervise them correctly. She only reprimanded the guy who arrested and dragged the guy, who wasnt even proven guilty, like dirt through the mud. They had no proof of anything. The guys who were blatantly harrasing the knights were left without any consequences. She was in charge, she did not correct. The knights were only reacting to them, while someone, who wasnt even proven guilty atp, was dragged through the mud.
She wants to lead the magic tower, how does she plan to do that, when they a small team whilest an investigation runs havoc like apes.