According to the nomenclature of coordination compounds, complexes in which a metal is bound to only one kind of donor group are known as homoleptic complexes (e.g., $[Co(NH_3)_6]^{3+}$ where only $NH_3$ ligands are present). Complexes in which a metal is bound to more than one kind of donor group are known as heteroleptic complexes (e.g., $[Co(NH_3)_4Cl_2]^+$ where both $NH_3$ and $Cl^-$ ligands are present). Since Statement II provides the correct reasoning that perfectly aligns with the definitions applied in Statement I, both statements are true.