I agree. I don't think there was any argument 'because' she found out about NH. From what I have read, quite a few people at the casino knew who he was. The only way it could be believable is if wasn't that she found out about it, but if she made some nasty comment about it- that triggered him.
But, it seems more likely that he thought it would make a good story. That he, as an innocent, wrongfully accused man just snapped at the injustice of the accusations following him around, and he just lost it when she searched on his computer and found the lies about him. That people would understand how that could make an innocent guy snap and kill another girl, er, um girl.
Considering that supposedly in Chile he told police that he and Stephany were robbed by men with knives who attacked only he (and I'm guessing no robbers were caught on the camera, so him removing her pants to imply a fake sexual attack didn't work).... it is pretty clear that every story he has told is a complete fabrication and lie. So what that leaves as being the truth is the only thing he has not said- that he simply killed her to take her money. He certainly seems like the type whose anger could turn a theft into a murder.
I really would like to hear his story about what he was doing coming out of the room with coffee, knocking on the open door, closing it, knocking again, and then getting the maid to open it. THAT will be a funny story, no doubt.
I have never believed the Natalee story played into this. I DO believe that he liked the attention he got from it and so his first defense mechanism was "I was wrongfully accused of murder, everyone hates me, I got mad and couldn't help myself, Pity me!"
I just haven't been able to decide WHY he murdered her.