Of course they have the right to go through your meds, this is for security reasons, they have the right to "go through" anything.

Personally, I think the agents in NZ etc must be morons if having some pills in a bottle proves anything about what they are. This whole idea of drugs must be in "original packaging" is just silly. I suppose if I wanted to bring in illegal drugs, I'd just stick them in a bottle I had from some common drug like a statin or hydrochlorothiazide and those agents would think that proved something.

They have the right to go through your electronics, bag contents, etc. because there is legal precedent that forms the underpinning for their measures. They have the right to ask you to take your shoes off because someone tried to blow up a plane using his shoes. And liquids. And a fake laptop. And so on.

They have no interest in checking the legality of your meds, and, as Christina points out, there is no practical way to do so anyway.

So then the question is, can you do harm with some pills? Unless and until someone tries to, those are not screened.

Screening and search ... a colleague had forgotten a knife in his bag and it was spotted at the third airport of the trip.
....

I found a Swiss Army knife in a pocket of one of my bags that had been on multiple trips with me. I forgot it was there.