There seems to be an issue with W3 Total Cache with New Relic enabled and how it interacts w/ another plugin called Stream. There has been some investigating gone into it and there's a specific way that you modify the $current_user->roles when the New Relic module is activated (doesn't have to have an API key). You can view my original thread to them here and you can view the investigation on their GitHub issue here.
If you could provide any further insight or a fix, if deemed necessary, that would be great.