The concept of "octoroon" seems less relevant here that the
one-drop rule.
If some or all of us present-day humans have
any genetic component that comes from Neanderthals,
it matters. It tells us something about where we have come from and who we are. It tells us something about the prehistoric relation between our species (or subspecies) and the other species (or subspecies) of hominids.
However, it would be scientifically impossible to "draw the line" definitively between present-days humans who do or don't have Neanderthal ancestry.
Another point mentioned in John Hawks' article
Neandertal Introgression, 1000 Genomes style is that Sub Saharan Africans too have some Neanderthal-like material in their "derived alleles" (the component of human genome
not shared by chimps etc.) The Neander genetic component in the Africans is significantly smaller than the Neander component in Europeans, Chinese, etc, but it is present nonetheless.
Hawks says that, in the case of the Africans, this genetic component can be explained as coming entirely from the epoch
before Neanderthal and Early Modern Human populations diverged, rather than from later cross breeding between Neanders and EMHs.
It is a scientifically conservative assumption, but still an assumption. Another possibility is that
all present-day humans have Neander-EMH hybrids among their ancestors. Africans just have fewer.
If the "one-drop rule" is applied, we present-day humans may all be Neanderthals.