The model of the pure one-pion exchange mechanism, which gives a good description of the GAMS results on the alteration of the S-wave π 0 π 0 mass spectrum in the f 0 (980) region in the reaction π − p→π 0 π 0 n with increasing −t, is compared with the recent detailed data on the m and t distributions of the π − p→π 0 π 0 n events obtained by the BNL-E852 Collaboration. It is shown that the predictions of this model are not confirmed by the BNL data. Therefore, the observed phenomenon should be explained by some different exchange mechanism.