Telling a child to stop doing something they are in the middle of doing - biting , hitting, treading on etc - particularly when another child is getting hurt as a result of that action - is not actually telling the child off, it is merely an instruction.
A raised voice or shout is necessary in order to stop the child in their tracks, particularly if the person who is watching and spots the other child getting hurt is not immediately next to them in order to physically separate them but a few steps away (and therefore a few moments away) from being able to help the child being hurt. This isn't anger, it's just rational because a loud noise will startle a child and therefore hopefully help to interrupt the problem behaviour.
Telling off is when the adult turns on the child doing the naughty thing and starts to tell them that they are being naught/biting etc is wrong, they should never do it again, go sit on the naughty step and so on. THis doesn't need to be done by shouting at the child - that would be when it goes OTT and angry. If the OP had ranted at the child and shouted at this point, that would have been anger and wrong. But it doesn't sound like she did this. And it doesn't sound like the child's parents made any attempt to tell their child that they had done anything wrong - either there immediately or by taking them out of the room to tell them and calm down.
I've read all through this thread and still can't understand what the people who say that the OP was wrong to shout or tell off dn should have done to have actively stopped the dn from biting her dd as the bite was in progress.
Should she have just sat and watched or wandered over and tapped dn on the shoulder to say excuse me, can you finish that now please? If they saw somebody hurting their child would they really not try whatever they could to stop the hurting as soon as they could?
I get that different people have different approaches to discipline and they may want to be trying an 'ignore this behaviour' approach for biting. But sure this doesn't mean that they ignore a child who is in pain whilst being bitten?