Brian Ferentz may officially report to Barta, but the idea that Barta has the power to fire Brian Ferentz is laughable. Barta is not going to do anything that Kirk Ferentz does not want. The only thing Barta has a say in is how much the assistants get paid, but even there Barta pretty much does what Kirk tells him to do.
If Barta ever threatened to fire Brian, all Kirk would have to do is threaten to retire and that would be the end of the discussion. Maybe if Iowa goes 5-7 this year, Barta might have the leverage he needs to fire Brian.