Claiming you shoot by accident opens up a can of worms involving a far lower legal standard to be held liable for any potential damages.
In Texas, I would go with trying to stop a fleeing felon and just missed (not in OK). My guess is a smart lawyer will try to get something involving at the very worst a small fine for firing in the city and perhaps a period of suspension for the carry license. IANAL
Was her life in danger? Doesn't sound like it. Was it accidental/negligent discharge? Doesn't sound like it. She pointed and fired at someone running away. She's lucky she didn't hit him. Or anyone else for that matter.