Neeks' power doesn't specify she has to give items to different players. As far as we know, she could have given the same person she trusted multiple presents.
And Reki has the ability to fact check, I figure it's our best chance right now to at least clear the roles of two people.
What we know so far:
N1: ligntning rod to exodus
N2: post restriction to exodus and possibly nin
N3: lie detector to reki
I think it is save to assume that she also handed out a bulletproof and a cop check since those seem to be the most valuable items. She probably thought the items handed out N2 would be sucked up by the lightning rod, so she just gave out two post restrictions.
Since there was no cop check claim on the previous days I assume she handed out the bp on N1, but I'm not sure she would just give reki basically two cop checks without a guarantee that he's town. Seems to make more sense to diversify your investments.
(fake edit: I don't think she could give herself items, otherwise she would probably have given herself the bp and it would also be kind of broken.)