Whether the integrity of the exams is actually guaranteed is immaterial, because the company that made the nanny software went on the record and took responsibility, and/or by splitting the responsibility, the school admin and the nanny software vendor can point fingers at each other and the responsibility essentially disappears like it usually does.
You can see this with most other security theater type things. As long the "general public" is unaware that they have been lied to, they will accept this kind of positioning as gospel, and not look into it further. For the most part, as expected, the world turns around just fine without real security because systems tend to be robust to a certain level of bad actors doing selfish and small scale bad things like exam cheating, and as long as nobody's feelings are hurt, it's all fine.