Band theory predicts both K3C60 and K4C60 to be metals; various experimental probes show that while K3C60 is indeed metallic, K4C60 appears to be insulating. The standard view of this apparent failure of the single-particle picture is that electron correlation is predominant. We describe an alternative scenario, motivated on theoretical grounds, which invokes a spin- or charge-density-wave state to explain the observed insulating behavior.