Recent observational studies linking variability in global ocean productivity with upper ocean warming are based on the paradigm that warming produces a more stable water column which, in turn, inhibits primary productivity for a large fraction of the global ocean, namely the tropics and subtropics. Though seemingly straightforward, this paradigm relies on the assumption that an increase in the stratification of the upper ocean water column decreases the vertical mixing or overturning of the surface waters such that the supply of nutrients to the euphotic zone is reduced, and so too the primary productivity. Here we show, using observational data in the North Atlantic subtropical gyre, that while upper ocean stratification and primary productivity are strongly linked on seasonal time scales, they have at most a weak correlative relationship on interannual time scales over the modern observational record. We suggest that interannual variability in ocean biomass and primary productivity depends on a host of variables that are not easily predicted from the expected temperature response to climate variability and change. These variables include the strength of local and remote wind and buoyancy forcing and the surface or subsurface advective supply of nutrients.