Your example is different in a critical way. These two questions are not equivalent.

Q1: I looked at only one of a pair of two randomly selected children and it was a girl. What is the probability the other I didn’t see is a girl?

Q2: I looked at both of two randomly selected children and at least one of the pair of children is a girl. What is the probability the other is also a girl?

The question in the article is the second question, not the first. The fact that the observer looked at both children and not just one of them is crucial. As is often the case in these puzzles the exact information available is the critical issue.