out of that school right away, ok?

Then go and find another school for your child. But before you enrolled your child, do the same procedure. Go to the reception and ask the same queries you asked in the current school. If you find it satisfactory, then nobody stops you from transfering.

Yes, you are not paranoid but you are over-reacting. Calm down and talk to the higher up as you were informed. And better talk to the teacher also, they are the one directly involved. I think you'll find a more sensible answer. But my suggestion, look around first and try to find what you are looking for before asking them.