Meaning of "that's fine" in modern American English when used as an answer to a question
Here in the States it is tricky due to the melting pot of cultures so "thats fine" could be interpreted as a simple acknowledgement/agreement to a passive aggressive way of showing ones upset/half-hearted agreement without actually saying the words. It all depends on the conversation. I would say in a professional setting, in general, it is used as an agreement/acknowledgement. Used in a personal setting its more looked at as rude... "can you watch my daughter for an hour, id appreciate it?" "Thats fine." This is a half-hearted or resistant agreement which comes off as "I really don't want to but I will so I don't appear selfish or rude."