You said it yourself: in the Court's opinion, Justice Gray added "unnecessary additional commentary." An examination of the Opinion quickly reveals that Sections II and III, which contain the bulk of Justice Gray's analysis and in your eyes are nothing but dicta, are long and detailed. Yes, joining a decision does not indicate agreement with every "sentence or phrase," but we're not talking about a word or even a sentence. We're talking about pages upon pages upon pages of dicta. Your reply is greatly weakened by just how long Sections II and III are. If the other five Justices felt that Sections II and III were unnecessary, they would've written separate or concurring opinions to express their discontent with Justice Gray's "unnecessary [and extremely long and detailed] additional commentary." They did not.
Given such circumstances, Justice Grey's unnecessary additional commentary about the natural born citizen clause in a case not addressing the question was in effect self-serving and an obvious conflict of interest, whether or not anyone can prove he was aware of the conflict of interest. So, no conspiracy theory is required to observe the obvious facts of the circumstances.
Well, it wasn't obvious at all to President Garfield, who chose Chester Arthur as his running mate. Nor was it obvious to Winfield Hancock, President Garfield's Democratic opponent in the Election of 1880. (By then, mudslinging had already become common in elections.) And last but certainly not least, it wasn't obvious to the 4,446,158 Americans who voted for the Garfield-Arthur ticket, or the 214 electors who cast their lot with the Garfield-Arthur ticket.
So obvious to you, yes, but no, not obvious to others.
If such simple cause and effect logic is too difficult for you to understand and be logically obvious, a person has to wonder how you can hope to understand how language, French or English, provides the inherent definition of a natural born citizen.