Actually you missed the point of the post.
Both of them were present at the temptation, Adam stood there and did nothing, said nothing and then participated in the fall.
Why does Pope place such significance on Adam’s fall, because Adam was in charge of the Garden and all things in the Garden. Note when we refer formally to the fall in the Garden, it is Adam’s Sin.
Read more here: http://blog.adw.org/2010/08/why-is-the-first-sin-called-the-sin-of-adam-not-the-sin-of-adam-and-eve/
So it is interesting to consider that the first sin, may not have been eating that dang apple, but in failure to fulfill one’s responsibility that God has charged you with.
Well said!