That's not at all what is happening in a crowd crush situation. As explained in the video, above a certain crowd density, people physically lose the ability to control their movement in the mass of bodies and involuntarily behave more like molecules in a fluid and less like individual actors. The people in the back of the crowd, who still have agency in their movement, don't know that they're indirectly causing the death of others, they're not homicidal maniacs (for the most part).
Blaming crowd crushes on the lack of "critical thinking abilities" and "commitment to some ideology" is intuitive, easy, and wrong. A wrong model for a problem will prevent you from finding an effective solution – as seductive as that model may be.