The classical impact theory of Gordon is used to calculate half-widths and shifts of spectral lines of the pure rotational band of 12C16O isotopologue broadened by He. Two rotational transitions are examined: J=0J=1 and J=1J=2 in the wide temperature range from 1.3 to 600 K. The main purpose of this work is the study of the validity limits of classical impact theory at low temperatures. Dynamical calculations were performed on the accurate CO-He ab initio potential energy surface. The results of calculations are in good agreement with experimental data with the exception of very low temperatures. The contributions of collisions of different types (elastic, inelastic, quasibound complexes) are clearly examined in the classical picture frame. It is shown that the mismatches between classical theory and measurements are caused by the too high contribution of elastic collisions into broadening and shift in the present variant of theoretical model. The idea in the spirit of the Weisskopf theory is applied to try to diminish this contribution. The classical results are also compared with the results of fully quantum close coupling calculations made with using four CO-He interaction potentials. The roots of discrepancies at low temperatures as well as the virtues and the shortcomings of a classical approach are discussed.