The way I understand it is that the moment the opponent starts into the "twirling" animation is like the moment a normal grab would attach to the opponent. Perhaps to stop this animation from being a liability to Kirby, they added some SA frames that simulate the effect of a grab having priority over normal attacks. (I'm pretty sure they do, if I'm wrong someone please tell me)
In every other way, Inhale behaves like a grab except for the fact that at a certain range it pulls people into "grab range". At this point Kirby does not have SA, however, because the "grab" hasn't happened. As for the case with DK, it may be that since the Punch extends his hurtbox with his arm, he placed himself in "grab range" for Inhale, you took damage but Inhaled successfully just as any grab would.