The analysis of negative birefringence optically induced in major air components (Loriot et al., [1,2]) is revisited in light of the recently reported plasma grating-induced phase-shift effect predicted for strong field pump-probe experiments (Wahlstrand and Milchberg,[3]). The nonlinear birefringence induced by a short and intense laser pulse in argon is measured by femtosecond time-resolved polarimetry. The experiments are performed with degenerate colors, where the pump and probe beam share the same spectrum, or with two different colors and non-overlapping spectra. The interpretation of the experimental results is substantiated using a numerical 3D+1 model accounting for nonlinear propagation effects, cross-beam geometry of the interacting laser pulses, and detection technique. The model also includes the ionization rate of argon and high-order Kerr indices introduced by Loriot et al. enabling to assess the contribution of both terms to the observed effect. The results show that the ionization-induced phase-shift has a minor contribution compared to the high-order Kerr effect formerly introduced, the latter allowing a reasonably good reproduction of the experimental data for the present conditions.