Personally, I'd tell her to stop yelling at my kid, because yelling is not an affective way to communicate, and teaches children to be emotional, rather than rational, during disagreements. I would then pull my son aside, explain that what he did was not okay, even though what she did was not okay either. I would ask him to apologize to her, even if she doesn't apologize back, and then tell him that he should always do the right thing even when other kids (and, ahem, adults) don't. Then, later, away from the kids, I would explain to my friend that was not acceptable behavior on her part. I don't think I would lecture her about not talking to her daughter about the shoving, but explain that if you see violence like that, you will calmly intervene to maintain everyone's safety, and that you will calmly explain the rule about no hitting to any child who hits.

I think parents should be able to correct other people's children, since safety is paramount and I don't see a problem with kids knowing that there is a network of adults ready to enforce rules, but corrections should be fair, loving, and calm. Parents should also only correct other people's kids if those parent's aren't around. You were right there, so it was your territory.