Let's put it this way, what reason does NSN have to lie about any of this?
As Yinfo said, it's not a big deal, he was just using this as an example anyways, what's the worst that could happen? Somebody worshiped by hundreds of other players (kakai) loses a couple hundred K?
Now, this is the first NSN V. Kakai thing I've seen so it's not an on running war of slander so that's not a valid reason.
If he was, and this is a long shot, trying to get Kakai kicked from Dunamis, it wouldn't matter much anyways or even work, I'm quite sure NSN is much smarter than that anyways.
He's poor? No I don't think he's so desperate for cash that he'd need to resort to loot stealing/following people around. And even so there would be no reason to "lie" about it.
from what we can see Kakai acknowledges what NSN said about inventory management and says that it's still his fault even though her inventory was full.
Now, here is how we can settle this.
NSN, Take a screenshot of your loot stealing skill, if it is at 0 then NSN would not be an effective loot stealer and this whole idea that he is/was following kakai and purposely loot stealing is not true.
If it is anything above 50% or so, not familiar with how high the skill goes, so I'd say that's reasonable point to say he might have done it but even at that he still might not have done that.