After studying protein denaturation by urea for many decades, conflicting views of the role of the side chains and the backbone have emerged; many results suggest that urea denatures by enhancing the solubility of both the side chains and the backbone, but the frequently applied transfer model (TM) so far ascribes denaturation exclusively to urea's action on the backbone. We use molecular dynamics simulations to rigorously test one of the TM's key assumptions, the proportionality of a molecule's transfer free energy (TFE) and its solvent-accessible surface. The performance of the TM as it is usually implemented turns out to be unsatisfactory, but the proportionality is satisfied very well after an inconsistency in the treatment of the backbone contribution is corrected. This inconsistency has so far gone unnoticed as it was obscured by a compensating error in the side-chain group TFEs used so far. The revised "universal backbone" TM presented in this work shows excellent accuracy in the prediction of experimental m values of a set of 36 proteins. It also settles the conflicting views regarding the role of the side chains because it predicts that both the side chains and the backbone on average contribute favorably to denaturation by urea.