Combining mean-field and renormalization group analyses, here we unveil the nature of recently observed superconductivity parent metallic states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields ($D$) [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 434 (2021)]. We argue that close charge neutrality, on site Hubbard repulsion favors layer an...