But it's a valid point, the question is not well-posed. If you said, "I looked at both children and saw that at least one was a girl" more people would get the right answer. Many people will assume that the author looked at only one child, not both. And there's nothing in the wording to indicate either way.
As others are pointing out, this is just the Monty Hall problem. But the way the question is posed there is much clearer.
I don't know how this could be made more clear:
"You're told that at least one of them is a girl"
> Many people will assume that the author looked at only one child
There is no mentioning of "looking"
The answer is: it doesn't matter how because that is an unambiguous statement.
It means "you can assume the family does not have two boys".
I think people are actually getting hung up on "you are told" as if that could be a lie, or some kind of trick, when it is really just supposed to mean "here is some more information that you can rely on".