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URu₂Si₂ exhibits a novel type of order below T_o ≈ 17K, with an apparent (BCS)-like phase transition in C_p(T), yet three decades of intense research have yielded no definitive signatures of any associated symmetry-breaking. Noticeably, a number experiments have also shown an electronic energy gap which closely resembles that resulting from hybridization between conduction electron and 5f-electron states. We argue here, using thermodynamic measurements and minimalistic modeling, that the above observations can be jointly understood by way of proximity to an entropy-driven critical point, in which the latent heat of a valence-type electronic instability at T_o is quenched. Salient features of the putative valence-type transition include a robust energy gap displaying highly degenerate features in the electronic DOS that is only weakly suppressed by temperature on approaching T_o, an elliptical (T_o,H_c) phase boundary in magnetic field and temperature emerging from the consequences of a clear Pauli-PM limit in the (same) electrons responsible for all T_o, quantum oscillations, and superconductivity and, importantly, the lifting of the requirement of a broken symmetry in the ground state below T_o in URu₂Si₂. Implications for other unusual aspects of strongly correlated electron physics will be discussed.