hi fearnelinen. I'm glad you picked up on the in loco parentis issue because I feel it's important as it affects the teacher-child-parent dynamic in terms of what is expected of all the parties concerned.
My take on it is this: when a child attends school, the school acts in loco parentis, "or instead of a parent." I take this as meaning that the school takes over the role of the parent, and deals with the children as it sees fit during the course of the school day. It does NOT mean, IMO, that the school necessary has to deal with issues in the way the real parent would like - that would be impractical - and that therefore parents have to accept that there will be a certain amount of give and take in the relationship between the child and the school. This is part of life, and most parents accept this. It also helps draw a line between school and home life.
However, there are parents who cannot, and have a different idea of what the school/ child/ parent relationship should be like. To be fair, this seems to be as a result of the recent blurring of the boundaries between school and home, and has been encouraged by schools in the main part, resulting in a variety of semi-formal "contracts" and the like between parents and school which has encouraged greater involvement from parents in school life. Unsurprisingly, some parents feel they then have the right to try to influence what happens in the classroom - I have friends like this, who are constantly complaining about the most trivial of incidents in school, undermining the teacher, and insisting that their child should be treated differently from others.
I'm getting on a bit and remember a time when things were completely different. Parents being involved in school was simply unheard of, and it was accepted that school life was school life, and home life was home life. The trust you talk of was implicit, and parents got on with their lives whilst the school got on with its job in loco parentis for the duration of the school day. Any poor behaviour at school was dealt with, and parents backed up the school at home by reminding the child what was expected of him or her (sometimes accompanied by the threat of something unpleasant happening "when your father gets home!!"). It may not have been ideal, but at least all parties knew the boundaries and respected them. Personally, i would feel very uncomfortable doing this, because I simply do not see what happens in school as my business (not because I do not care, incidentally!)
It's more difficult these days for teachers IMO, because not only do some parents feel they have the right to challenge the school's authority when in loco parentis, but children themselves seem to have been accorded more "rights" to consultation and involvement etc which have resulted in a further blurring of teachers' rights to assert authority at school.
On the point of the OP's child's behaviour - I'm not sure shere she's coming from on this. Is she complaning about what she sees as poor handling of the incident? If it were me, I would not be happy about fighting in school, and embarrassed at the behaviour. I would want to actively support the teacher, not by getting involved in school politics, but by making sure the child understood what behaviour is expected and if he then chooses to misbehave, what the consequences would be. Apologies if I've read the thread incorrectly, but the OP, IMO, is not only acting inappropriately by challenging the school, but also condoning the fighting itself.
I speak as a teacher and as a parent here - in no way was the action of this teacher professional - but, as I'm sure you will notice as your own teaching career progresses, every teacher starts their career with the best of intentions but in many cases do not have the tools, even if well-trained, to deal with the barrage of poor behaviour that is a feature of their working lives, made more difficult by the culture of entitlemement that many pupils and many parents now seem to have.