The school might know it is not true because (for example)
The child alleges that Mr A did action B on day C but the school have on record he was ill at home that day
Or that he was teaching another class at the time.
However the school will still have investigated whether it might have happened at a different time.
I worked in a secondary for many years and we actually employed an ex-police officer for exactly this reason,
Let's say child A alleges that teacher B hit him. In my school all the children in the classroom would be separated out and asked to write their account of what happened in silence. This means there's less oppportunity for collusion.
The advantage of working in a school is the incidents are normally witnessed by 30 plus people. Teachers are generally advised not to speak to pupils alone, at least in part so that if false allegations are made there is another witness.
Many schools also have cctv which covers the playground/entrance so the school might know it is not true because they literally have video evidence of what happened.
Children lie. All the time. Sometimes intentionally, sometimes not, cctv and the written statement system usually finds most false accusations out,