Fame does not equal trust. While there may not be any security through obsecurity it is a barrier. As for being a trusted CEO at a certain point its about who you know and who knows you. Do you think the NSA employees all have social media profiles?
Fame doesn't equal trust, but trust over time does create recognition (perhaps fame is a bit too strong). My claim is that if no one can vouch for you, how can I trust you?
Fame doesn't equal trust, but if someone with no public background starts claiming to have been in the NSA/MI6/FSB/whatever, why would you believe them?