The answer is:
James Cross Giblin’s word choice shows that he respects Champollion because he states that Champollion was proven to be “correct without any doubt” and he describes Champollion’s book as “ground-breaking.”
The narrator best backs his claim with evidence because it proves with reasons and quotations why Giblin respects Champollion. Thus, he provides Giblin's actual words which describe Champollion as "correct without any doubt" and his book as "ground-breaking," meaning that he admires his veracity and novelty.