Think you are misunderstanding what they are counting. The bristles of the seed sit on a stalk and are quite visible individually for the most part, because they are quite thin and stick out in different directions. If you were to place it so that the stalk points toward you, like in the Nature video, the bristles would stand out really clearly.
I think the real question is, which is more cost/time efficient:
a) Hire someone or a company skilled enough to whip up some classifier that can count these from some accuracy, level, which entails paying a developer, and probably 5-10 graduate students to sit around and count dandelion bristles on a good number of dandelion seeds to create a training set.
or
b) Just have 5-10 graduate students sit around and count dandelion bristles on a good number of dandelion seeds
Given that a is a super set of b, and the extra portions of a are likely much more expensive than all of b, I think the answer is fairly clear...
Hm. Are NNs reliable enough to be sure you're getting a correct result?
I'd imagine this kind of task would lend itself to some old-school image recognition techniques - photograph against uniform background, threshold, mask the middle part and count contiguous regions.