It's a simple argument. Most people would trust David Attenborough's authoritative voice over a total stranger's voice. I'll surmise this would be true even if they knew nothing about Sir David.

Not sure what you mean here, but if you're saying that people who know nothing about David Attenborough would trust his voice because if its quality, I couldn't agree more. It's vastly better than the voice on the video.

Are "thinking" people really the problem here? Most thinking people I know are already agnostic or atheist.

There are many intelligent, thoughtful people who are not atheist or agnostic. Of the 80% or so who retain religious beliefs, we should be aiming such videos at those most likely to be persuaded by reasoned argument and calm, thoughtful commentary. Hyped-up commercial voice-overs won't help.