A detailed photoluminescence (PL) study reveals a striking similarity in local vibrational properties of a defect center in GaN as compared to that for the substitutional OP donor in GaP. This observation could be interpreted as if the center is in fact related to the substitutional oxygen donor in GaN. The deep-level nature experimentally determined for the defect center calls for caution of a commonly referred model that the substitutional oxygen donor is responsible for the residual n-type conductivity in GaN.