I don't if you've read the article, but in the part just above the part 2.5.1 activating the tool you can read something about the threshold. In short it says; when there are colours in the picture which are very the same (for example, although these are quite big differences, yellow and orange), and you want to select them both you can adjust the threshold. How bigger or smaller how more the difference between colours can be, or how more it's just only one colour. Just play with it until you get your result.
BTW you could also select the white part, then press shift and then select the white on the edges, now it will select both colours of white.
p.s. I'm speaking of colour, but ofcourse white isn't a colour. Luckily gimp and photoshop don't nag about it.