We can pretty much count out Godly influence as a motive of atheists. I'm sure there are exceptions, but I think most have no compunction from the Spirit, they have a group; notice they all say the same things, meaning they have a bandwagon, sports fans mentality, so they develop an enthusiastic jocular attitude which fuels their attacks on the Bible. So the motive to be truthful and question their own pattern of behavior is practically non-existent.
So why would an atheist step back and try to be fair? I don't think it is a reasonable thing to expect. Though there are always a few that might actually respect truth. So your question might have a good influence on a small number of them.