Sorry, but the paragraphs that follow support the quote. You’re confusing yourself over an independent clause.
Please read up on what an independent clause is
An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.Do you think this is a whole sentence? "That neither Mr. Justice Miller nor any of the justices who took part in the decision of The Slaughterhouse Cases understood the court to be"? Obviously not. The clause can't be removed without damaging the meaning, or you wouldn't have needed to do what you did, substitute "Justice Gray affirmed" for what the beginning actually said.
You can't gloss over the fact that you butchered the quote to make it say the opposite of what it really said.
The paragraphs that follow do not support what you think they do. But it's hard to continue discussing with someone who thinks it's fine to butcher quotes to reverse their meaning.