However you define it, a central nervous system or other type of similar central unit would have to be a requirement, because that is what would actually be sentient

Without CNS there would be something else sophisticated enough to show sentience that would have been sentient. So to me it looks like this is not really a requirement, albeit it's simpler to say that it is.

As a side note, I think that given how human-centric humans are (which is to be expected, really) even if we were living with another sentient species on the same planet we would argue they are not sentient for whatever reason we could come up with, and change sentience definition accordingly