As weird as it may sound, I think that the statement is probably correct (I am not sure since I haven't check it directly, see below). The kinematical dependence may be different in the two cases. For example, imagine that the scattering amplitude for the first process depends only on the Mandelstam variable $s$, then the scattering amplitude for the second process is related to the first by crossing symmetry which, simplifying a little bit, exchanges $s$ and $u$ variables. Now, $u$ depends on the scattering angle, whereas $s$ does not. You can thus see how the different behavior in the scattering angle may arise. I must say, however, that I haven't calculated directly either one of the two scattering amplitudes, so while I find the statement highly plausible, I can't be completely certain about its specific validity. If for example instead the amplitude for the first process was depending only on $t$, than there should be no difference in the two processes.