Pedantically, they don't merge, you just rule out GB or BG. So, initial conditions:

    1) X: G, Y: G
    2) X: G, Y: B
    3) X: B, Y: G
    4) X: B, Y: B

If you are told, "at least one is a girl," as in the posted question, you can only rule out case (4). If you are told more specifically that X is a girl, you can rule out (3) and (4), giving the 50-50 chance.

Which still seems a little weird to me, that knowing which is a girl, regardless of which one you know about, changes the chances.