I would hope that the school would only act if this is proven beyond any doubt, not based on hearsay, and with review of the whole incident. Things can appear very different without any lies being told - these 2 incidents come to mind -
A child in my daughters class accused a teacher of pushing and grabbing them. The parent came in all guns blazing and demanded the teacher was sacked. The other children in the class were interviewed, and it turned out that the child (with additional needs) ran towards the teacher, there was some water on the floor from ? a childs water bottle, the child slipped and the teacher instinctively reached to protect them from hitting their head on a nearby table. So yes the teacher did 'grab' the child, but it was protective, and yes the child fell but they were not pushed.
In another incident, a parent went round our village saying an LSA had forcefully restrained and hit their child. The reality was this child was beating up another to point they had to go to hospital, and the LSA was restraining them to avoid them hurting another child even further, and they ended up also injured in the process.
People can share their stories in a way which isn't lying, but isn't sharing the whole truth either. In both these scenarios the parent did not lie, the teacher did grab the child (to try to stop them hurting themself) and they did restrain a child, but these were well intentioned and proportional responses.