I can't believe this thread and all the assumptions that have been made yet knowing next to nothing of the circumstances. We don't know the age of the child, the relationship between the child and SF, the circumstances by which they informed someone at school of being scared, whether there are any issues with the child, how long they've been together etc... I'm not surprised at all that OP hasn't wish to come back.
For all we know, the child in question is 14, with an attitude having been spoilt by mum and SD is trying to install some discipline in her life, supported by OP. Maybe SD doesn't like it that her SD has said that she can't go out to meet her boyfriend at 10pm on a school night and screamed at her when he saw her trying to climb down her window because he was scared she was going to be hurt. SD hates him for preventing her to see her boyfriend and decided to report him being vindictive.
This is as likely as the child being a 6 shy six year old who is being verbally abused and threatened by her SD, most of it when her mother is not around and broke down in tears in front of her teacher after he told her the previous night that if she said anything to anyone, he would make sure that her mum would get hurt.
We don't have any idea!
By the way, I am a shouter, owed to my Mediterranean background and yes, I use it as a form of discipline and it works very well. My kids are not scared of me at all, but like many, they will try to get away with everything and after being nice, negotiating etc.., it is often shouting that gets them to take me seriously. They are now grown up teenagers, very contented, confident, secure and well behaved and we have a great relationship. They do know though that if I ask them 3 times to bring their dirty clothes in the basket, it is highly likely that the 4th time I will be shouting at them to do so!