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.
Well, that remains to be seen. Looking at both websites, it's difficult to tell what they are talking about. Flat-UI doesn't seem to have any assets that mirror anything on LayerVault's. They need to be more specific.
> Flat-UI doesn't seem to have any assets that mirror anything on LayerVault's.
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.