Does a nonessential phrase affect the pronoun?

Solution 1:

I think you are correct in this case, and that the author (who really ought to know better) is wrong.

Cecilia, along with the others, was wrong about Daisy's role in the fiasco at the game.

It, along with many others, was a dark and stormy night, and the rain fell in torrents, soaking Snoopy and Ms. L'Engle, who were soon to be among the great washed.

Glen and his friends took their first trip to Hawaii that year.

Solution 2:

"along with his close group of friends" is parenthetical, which means that, as you say, it is "nonessential", and removable. Take it out, and the sentence should make sense: "Glen took their first trip..." is, however, incorrect.