There's been some debate on whether Herschel Walker actually does what he says he does....I think he also claimed to only have one meal a day of bread, soup, and salad. LOL..complete violation of thermodynamics.
Anecdotally, I've seen plenty of people doing only calisthentics look fairly good with low body fat (e.g. ex gymnasts, the folks from BarBarians or the ghetto workout series, circus acrobats). Don't know how much genetics factor into the equation for these folks or whether they lift weights and you ignore that.
I've done the 100 chins/200 pushups program daily in the past and I guess I made some noticeable improvements after a month. I suspect this is not the ideal method for hypetrophy/aesthetics though... Otherwise I imagine all bodybuilders would just do high volume bodyweight pushups and pullups all day.