I think on balance you're probably right - though I'm not sure I agree with your conclusion that she should've been fired and I'll explain why.
Lying to the police is a serious crime but lying is a complicated thing because although your subjective truth might be out of whack with objective reality you're only guilty of lying if you deliberately mislead. I think in this instance she probably did exactly that and we've been here before with Emmett Till et al. However there's always antecedents and tbh, I was expecting her to release some sort of statement about being harrassed by men in public places in her defence and some sort of contextualisation that reasserted her status as the victim.
The reason I wouldn't have fired her is that I don't believe in the spread of personal transgressions into a wider punitive collectivist action. It has too much scope for puritanical over policing. You're right though, she couldn't have been trusted with being in a position of authority. If she'd disclosed it to her workplace - as she probably had to do (rather it arriving by a mob campaigning for her head) then it would've been put on file and been something worth watching more closely. At the slightest hint of a complaint from any BIPOC employee about her racism, she would've been hauled over the coals and fired for that. The police report being part of the case against her. If it's a pattern of behaviour (and it probably is) then that is what you nail her for. No complaints, no fuss, no press, pack up your desk Amy... we're done.
Instead the right wing has a martyr and she still continues to paint herself as a victim - and will do in perpetuity. Because in grey area cases where one facet of identity is held against another, the victim statuses would always be polarised and unhelpful ammunition would be equally distributed amongst both sides.
There was a learning moment here where restorative justice could've produced a better outcome. This escalated because of the way both of these individual behaved in the public setting. The learning point for her was that there's an element of her personality that when pushed will come out swinging like the KKK. She needs to address that but I'm not sure public humiliation is the best way to do that. Cognitive dissonance is too strong a force to allow that.
And for him, the learning is... perhaps let qualified people police the behaviours of others in public. If you're carrying dog treats around (and you don't own a dog) then you're clearly out in some sort of canine vigilante capacity. People are irrational about their dogs, they are like children to those who love them. If approached by Christian who was telling me to leash my dog I would've told him politely (at first) to fuck off. If he'd tried to call my dog over and feed my dog, I would've punched him in the face. Not because he's black, but because (as you've rightly said) he behaved like an asshole.
I guess we're in agreement that nobody came out of this looking great. We've come to different conclusions about how it should've been handled. That's the joy of two argumentative people dissecting the world politely. :o)