Without knowing the school ethos and standards it’s hard to comment. The video likely shows pupil A assaulting pupil B. If the school has a policy of excluding all students who assault other pupil regardless of the circumstances, then it is probably prima facie evidence and any investigation is going to be quick. Arguably witness statements, including those from the two pupils, aren’t necessary to complete the investigation in to the conduct of the OPs daughter. They may be needed to investigate other pupils behaviour.
This wouldn’t mean the guidance recommending a meeting with the child isn’t necessary. But the guidance allows discretion on this stage. The HT should really record why he is exercising this discretion. And we can only guess what this was if it was a conscious decision or an oversight. The OP should be asking questions not making accusations or jumping to conclusions.
If I was the OP I would want to establish whether the school has a zero tolerance policy that means all pupils who assault another pupil are excluded or whether the school applies a case by case determination. Again the OP should be asking questions.
The OP should inform the school of her daughter’s accusations. But in the absence of video, her daughter is going to need people to come forward and confirm this. She is going to need people to use active statements, not “a fight broke out”, “got in her face” or they were on the ground. She does need the investigators to push for clarity on passive statements.
I don’t like people in authority using powers given to address extreme situations being used to make life easy for them or make examples (thus making life easy for them). The HT and governors have been given sweeping powers here and they should be mindful of overreach in how they exercise them.