The figure below shows the fitted centroid of the pi^0 mass peak versus pion p_T for the 2006 data set (red, Weihong's analysis), the 2008 data set (green, from Justin), and for the gamma-filtered MC events generated by Mike et al.

All three analyses used the same algorithm and cut parameters, as well as the same fitting function (skewed Gaussian [same skewness] plus simple exponential).  The extracted pion mass is not only constant in time, but constant in p_T, for both real data and simulation.