Perhaps Nate is right when he says the moment is “already gone” since the moment Claire’s family pose for the photograph it moves from the “essence” of the experience to a construction of the experience. For example, in everyday life, when people pose for a photograph they may smile for the camera. There’s no inherent natural reason to smile for a photograph, but we become socially conditioned to create an impression of ourselves for the camera. In other words, the subject becomes self-aware of the impression they want to make. This is contradictory to Claire’s intention of capturing the essence moment and illustrative of what Nate means because as soon as Claire points the camera the choices of the each subjects pose is constructed as well as Claire’s framing of the image is a construct as well. The photograph defeats the genuine nature of the experience. But then, as viewers how do we know what Claire’s actual INTENTION other than what we think it is.
With this in mind, this scene may be self-referential to the show as a whole considering the viewer, who the show no doubt considers with it’s intelligent scriptwriting, is no doubt watching a television show which is, in fact, no more than a fictional construction in itself made up of thousands if not millions of photographs displayed in a ephemeral/time based manner which cannot be grasped.
Theoretically speaking, memory is fragmentary and therefore a photograph could never actual capture experience, especially when mediated through a camera. But then again, all experience is mediated through the social construction of language. With that said, maybe the photograph is no less authentic than the moment itself, whether it is fragmented and missing data or not.

actually nate didin`t say anything, he was dead, that was claire imagining him saying this

happy birthday!