There's a distinction to be made between counting on one's fingers and communicating a number with one's fingers.
You can easily communicate numbers 1 through 10 to just about anyone around the globe by holding up the corresponding number of fingers. But when it comes to 11 and up, you're generally not going to be able to communicate those numbers in a universally recognizable way. (Although "flashing" one's hands to represent intervals of ten is somewhat well understood.)
On the other hand, it's possible to use your fingers to count to numbers higher than 10, using whatever system appeals to you, regardless of whether others can understand it. The article talks about using the segments between each knuckle.
There's even a further distinction to be made here, though, between using your fingers to count and using your fingers to maintain state. You might, for instance, be able to easily use knuckle segments to count. But to maintain state, you need to make some movement with your fingers (e.g. bending a knuckle) with each transition period and then hold that new position for some period of time. And that can be hard to do with many finger positions.
You can easily communicate numbers 1 through 10 to just about anyone around the globe by holding up the corresponding number of fingers. But when it comes to 11 and up, you're generally not going to be able to communicate those numbers in a universally recognizable way. (Although "flashing" one's hands to represent intervals of ten is somewhat well understood.)
On the other hand, it's possible to use your fingers to count to numbers higher than 10, using whatever system appeals to you, regardless of whether others can understand it. The article talks about using the segments between each knuckle.
There's even a further distinction to be made here, though, between using your fingers to count and using your fingers to maintain state. You might, for instance, be able to easily use knuckle segments to count. But to maintain state, you need to make some movement with your fingers (e.g. bending a knuckle) with each transition period and then hold that new position for some period of time. And that can be hard to do with many finger positions.