How to actually invert the fuzzy selection?

[andreim]

For that particular case, as it didn't require a great deal of precision, I got away with it by using your procedure. But in most cases there's a difference unaccounted for, as @Ofnuts pointed out in the first reply. Initially I didn't get what s/he meant.
I've tested different ways to invert alpha and selection with different results but surprisingly haven't yet found a way to get a perfect "complement":

https://ibb.co/pvJQ74Z

And of course by "perfect" I mean a complement that totally blacks its counterpart.