TBH I think your DH was wrong to approach the child and "have a word" (quiet or otherwise)- it's not appropriate for him to be doing that (and for all you know neither your DS nor this girl have told their parents the whole truth). Especially if you know that your friend finds him intimidating (and that is likely to be because he IS intimidating towards her, from what you have said). If an adult woman finds your DH intimidating, I can imagine him "having a word" with her child would be pretty unpleasant for her. And intimidating for a child (even allowing for the fact that children will often cry when caught lying or if they are getting in trouble), especially if she is aware her mum is on edge/upset. Perhaps she reported it to the school because she was upset at what happened or because she thought your DH may approach her child to tell her off again/in the future, maybe when she was not present, and this worried her?
I would not march up to a child who had upset my child and "have a word"- it's just not the right thing to do. I would either have a word with the teacher about what had happened or would have spoken to the parents directly (generally, where an issue is in school I would approach the teacher about it). I would not challenge the child directly as a first response.
You- or your DH- should have spoken with your friend and said that you think her DD hadn't quite told the whole truth about what had happened the previous day because she and her friend's had been mean to your DS all day, which then escalated to him threatening her with getting your to "sort her out". Whilst you absolutely accept your DS was in the wrong too because this girl being unkind to your DS doesn't make what he did ok, you would like them to talk to DD about teasing your DS and then lying about what had happened.
If you and/or your DH did not feel that your friend would deal with this appropriately, you should have approached the school about the event- explaining what happened and that you aren't condoning your DS's actions, but stating your concerns about the girls' (friends DD and her friends) behaviour towards your DS and ask them to keep an eye on the situation.
I also think you do need to think about your DH's behaviour- he ignores your friend because he doesn't like her. Worse, he encourages your children to do the same. What kind of example does this set to your children? And why would you tolerate your DH acting that way towards your friend? He doesn't have to like her at all, but he should treat her with basic decency because she is your friend. I'm surprised your friend remained your friend for any period of time, TBH.
When you add in that people avoid you when he is around -and the fact that even you think that is because others don't like the way he acts or speaks to them- then this makes me think that your DH needs to evaluate the way he treats other people. And, in all probability, the way he is with you.