“I have let Whitman alone”

That's the opening stanza from Leaves of Grass, the Ur-text of American poetry. The opening stanza doesn't convey Whitman's break with convention fully, but it stands in for the rest, which does. And certainly these lines -- self-celebratory, all-encompassing, without conventional rhyme or meter -- convey an expression of independence!

Shhhh, if you admit you don't see it the game is ruined. Instead you should build on it, like improv actors in a jam session.

I'm pretty sure that two sentences you quote don't form a meaningful pair, so I wouldn't expect the second sentence to explain the first.

The sentence "Whitman was unequivocally declaring his own independence from poetic conventions and niceties." relates to what Whitman was doing, i.e. to announcing himself as "American, one of the roughs" in an earlier sentence.

"... Every atom belongs as good to you" corresponds to the later phrase "Here was a poet of the people for the people". That's my reading anyway. The structure is ABAB: quote, quote, gloss, gloss.

That was Samuel E. Clements, not Samuel L. Clemens, and Whitman wasn't involved; he was just an apprentice for Clements at the newspaper Clements edited.

Clements did succeed at digging up the grave, but apparently the mold and busts were destroyed during an argument over money.

Source: Walt Whitman's America: A Cultural Biography by David Reynolds