If you search for recorded velocities of the 22 mag vs 22LR from 4-5 inch barrels, you will find that the 22LR will give 900-1100 fps, the higher number usually with lighter (32 gr) rounds. In the same barrel length the 22 mag will give an average of 1350-1400 fps with 40 grain loads. So, the 22 mag has significantly greater MV than does a 22LR in small to midsize handguns.
However, short barrels -2-3" will lower MV to the point where the advantage over 22LR is probably not relevant for SD. No question that the 22 mag is best as a rifle round. Can it be effectively used for SD? - Yes. Is it the best choice? - Probably not; it is distinctly inferior to a 38 spcl wadcutter round. It is foolish to speculate whether the "5 shots to the head" story suggests inadequacy of the 38 special without knowing many more details, as other posters have pointed out.