Can modern cosmological observations be reconciled with a general-relativistic Universe without an anti-gravitating energy source? Usually, the answer to this question by cosmologists is in the negative, and it is commonly believed that the observed excess dimming of supernovae relative to that in the Milne model is evidence for dark energy. In this paper, we develop a theorem that clarifies the conditions for such an excess dimming, based on which we argue that the answer to the above question may counter-intuitively be `yes'.