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We prove that the motion of a single hole induces SU(N) flavor singlets in the U=∞SU(N) (Fermi) Hubbard model on a Husimi-like tree graph. The result is generalized to certain t-J models with singlet hopping terms typically neglected in the literature. This is an SU(N) generalization of the “counter-Nagaoka theorem” introduced in [Phys. Rev. B 107, L140401 (2023)2469-995010.1103/PhysRevB.107.L140401]. Our results suggest the existence of resonating flavor singlet (RFS)-like polarons in the t-J models on a more realistic nonbipartite lattice. Such RFS polarons may be relevant for a novel strong-coupling mechanism of superconductivity or other exotic fractionalized phases of matter.