The Go World article says that Black loses a very important liberty if he throws-in a second time. However, we cannot follow this statement.

Here, we have marked the liberties of Black's group in the upper right () with the classical sequence, i.e. without second throw-in. Please note that we inserted the forcing exchange of / , to clarify that cannot be counted as Black liberty. Black's group has 22 liberties.

After the second throw-in, the number of liberties of Black's group at top right () is still the same, 22 liberties. Black's top right group, and White's -group below (in the seki), do not share common liberties.

Within the temporary seki (we inserted the forcing exchange of /) White's -group, and Black's -group, share two common liberties ().

In the classical line of play these two groups share two common liberties (), too.

So, the relation between Black's, and White's, liberties remains unchanged, regardless of whether one or two throw-in have been played.