It is not arrogant to assume your child won't be allowed out on the piss at 12.
But it is arrogant to assume your children would never lie to you about there whereabouts.
I was the 'good girl' at school, top classes, top grades and my mother no doubt thought she'd never have to worry about me but from the age of 14 I was regularly telling her I was sleeping over at a friend's house when in reality I was out with boys. I remember once, when I was about 15 I stayed in a B&B with two of my friends (same age) and three guys that we'd met who were all 17/18 years old. I didn't have sex with anyone (not sure if my friends did) but it highlights that it goes on and the gentleman who offered us the rooms didn't ask for any proof of age as me and my friends all looked older than we were.
My mother would be horrified if she knew what I used to get up to as in her eyes I was just her well behaved daughter who stayed out of trouble.
Yes the 12 year old shouldn't have been out late at night but teenagers do lie about what they're up to in order to keep parents/carers in the dark.