She said she thought she ended up completely on her own because the teacher does not know about the lunchtime arrangements.
So had the teacher actually told her what time to be there, or had she gone to the classroom when she thought she should, found no one there (not at all unusual at lunchtime) and just sat down and done what she needed to? I think that is the central point here - a child could easily wander into a classroom at lunchtime alone; but if the teacher knew about it and was happy for her to be alone, maybe that is a different matter.
There are 2 views on it if the latter is the case. In this country, we tend to have rules which mean children need to be supervised at all times apart from when they are on the toilet. This was clearly not done and so you would have grounds to complain. And I think the complaint would be upheld and you would get an apology. That said, I think your daughter showed laudable initiative and did what was required of her with no fuss, and personally I would be praising that - she sounds quite 'sorted' over it which to me is quite sweet.
A friend has just come back from Norway where her Norwegian friend's 7 year old walked home from school alone each day, like all his friends, with a key hanging round his neck to get in when he got there. In Denmark very small children are allowed out to play at nursery, with no adult supervision, no fences and locks and no signing in procedures, no police checks for casual visitors etc. The staff watch from a distance, and children know what they must do if someone is hurt or unhappy.
'Safeguarding' has become a real issue in this country and we tend to handle it by means of rules, procedures, checks etc. Much legislation here is now designed to 'safeguard' us from each other and from Bad Things. Other places may do it differently, by trying to foster a community spirit and encouraging children, from their earliest days, to be independent, to care about each other and to help each other out.
I think this is a very interesting question Mystery, but perhaps not in the way you intended it to be.