past the thing which is annoying here is that the OP's DD has been misinterpreted and the teacher has actually exacerbated a situation needlessly. Probably with the best of intentions, but she needs to personalise what she does for each child.
Situation - child in line crying.
Typical response - let's talk about this, child goes off, it's sorted.
BUT OP's child DIDN"T WANT to talk about it. This is common in children with social anxiety who aren't crying for attention or for interaction. It is not heinously rude to not want to discuss why you are upset. I am the same. On the rare occasions I have been upset at work I have hidden in the loo for a cry. I would hate it if my boss came in and asked me to 'talk about it'. I would be mortified. We are all different. So, let's replat the scenario:
Scenario - OP's child, well known by her teacher, in line crying.
Teacher checks with her, 'Would you like to talk about it?'
Child - 'No', turns away
Teacher - - realising that this is THIS child who doesn't like much attention - OK, well I am here if you would like a word later.
See, no escalation, no assumption of rudeness.
Where it went wrong was in teacher's switch from 'concerned teacher' to 'affronted teacher' in assuming that this child had to speak to her and had no right to say no and turn away. This was interpreted as rude and OP's DD was then 'in trouble'. It was a non-situation escalated by misinterpretation:
scenario - child in line crying
Teacher - let's talk about this
Child - I don't want to, turns away
Teacher, affronted - Don't you walk away from me young lady, grabs arm to prevent this
Child stumbles.
Result - baffled child unsure why teacher is cross. Needlessly cross teacher. All because no-one asked the child IF she wanted a chance to talk about something, but assumed she SHOULD talk about something.
Unfortunately this is not a rare scenario. Some (NOT all) teachers would benefit from learning to personalise their responses and understand that they too have a responsibility to avoid escalating a situation.