This policy has been there since the beginning of the App Store.
If you use a private API they will reject the app. If you try and hide the fact you are using private APIs after has told you to stop then they will ban you.
It's all very common sense and not arrogant at all.
This is just a phrasing of a sentence in a mail. It does not define either what reasons they are allowed to ban you for, nor does it define what reasons they will use to ban you.
They are allowed to ban you for literally any reason. What matters is what they do, not the exact phrasing in a random email.
And in practice, they will ban you if you actively try to skirt their rules after they tell you to cut it out.
