Well, your "side" has one person claiming Brown moved towards the officer and that hasn't stopped them from taking that info and turning it into claiming/believing Brown charged him.
What is the more outrageous scenario?
Whichever one is more unlikely requires a larger burden of proof.
If we see an apple sitting below a tree, we don't have to rigorously detune someone claiming the apple fell from the tree.
If there's an orange sitting below a tree and someone claims it fell from an apple tree, we might be more questioning of one witness vs another if one claims it fell from the tree and one says it didn't.
An officer shooting a fleeing unarmed man or a man with his arms up in surrendering pose is not a typical or expected situation, the officer shooting a man charging him is the expected situation. It's just the way it is.
The different narratives are not equally plausible. Sorry, this is just the way it is. Most people know this which is why the case has attracted attention, if the man was shot dead while fleeing or surrendering it is absolutely outrageous. What it isn't, is likely.