I scratch constantly and so does DS. We don't have lice. We have eczema.
Also worth pointing out the scratching is caused by an allergic reaction to the lice bite. Not everyone who has lice will be allergic and itching.
I suspect daily antihistamine users will have less of an itchy reaction too so if they are carriers they won't necessarily itch.
Itching is not an indicator of lice so making an assumption that child A who is scratching like mad has lice when it could be a number of things inc eczema is a bit daft and cruel to the child.
The only way to know for sure is to look for visible signs - the eggs and the lice themselves.
Also suggesting every child in a class should be treated with chemicals at the same time is a daft idea too. I'm allergic to those treatments. They made my head sting, itch and I developed sores on my scalp.
The parents themselves may have lice too so that won't stop the spread.
Again. Lice are a nuisance and are harmless unless severely infested. Wet comb your child's hair regulaly.
Recommendations here are every other day if lice are found for 2 weeks. After that it is suggested you wet comb weekly to spot early infection and begin the 2 week cycle. But not everyone can manage that regularly and they shouldn't be punished. Hell I've had weeks where I haven't had the time to check beacuse work has taken over our lives and I've barely seen DS just to keep a roof over our heads. Many families will be in the same boat.
Tbh though, I'm really not that bothered about my DS getting lice. It happens. We treat. I don't judge any other family if they have them and wouldn't dream of singling them out or discussing with other parents that so and so is passing on lice we should do something. 
Compassion over judgement.