What he said is that he is "the exclusive rights holder for the artwork contained within Flat UI". Presumably he's referring to Flat UI the UI Kit, not Flat UI the general trend.
All of their assets were created in-house by DesginModo's designers..
I would say that is the issue in a nutshell. LayerVault is claiming they are the exclusive rights-holders, yet absolutely nothing in Flat-UI is the same as anything on LayerVault's public site.
The only possible angle remaining would be if LayerVault had a bunch of these elements behind their paywall... something tells me that's not the case.
Edit: Alright, I admit the colour Turquoise is used on both pages. Still, I'm fairly confident turquoise boxes (of differing shapes!) are not copyrightable.