It wasn't directly cribbed (unlike Western alphabets), but given that Hangul was invented in the 1400s after exposure to Western alphabets, most scholars still consider alphabets to have only been invented once [1] and then copied, much like the wheel. Although I suppose that's true of Cherokee too!
I think the idea is that since the inventers of bopomofo were exposed to other alphabets, it's still considered a descendant alphabet. I usually think of descendant as something that visibly manifests its ancestry, so for example modern traditional characters look somewhat like the earliest Chinese characters, or, all romance languages sharing some sounds or even words. So maybe we need a different way to describe things like wheels and alphabets.
1: https://en.wikipedia.org/wiki/History_of_the_alphabet