In other words, the reason NAT is seen as security is that it provides security (imperfectly, like almost everything else).
It doesn't actually do that.
You don't need to take that on faith either -- you can just test it.
How do you want to go about doing this? Although, 100% of the time people have asked me to do this they chicken out at actually doing it, so I suppose you will too. You might prefer to test with some network namespaces instead.