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...because if you're following at a safe enough distance, you won't hit someone even if they slam on the brakes. That's the entire concept behind many of the tactics promoted by safe driving education.
Totally agree with you and I really hate when someone is tailgating me.
Now, it's still important to know why the lady ahead just stopped in front of him; at least to me. If the woman was putting on makeup and got distracted enough to make her slam on her brakes then she should be at fault. People do that and all kinds of mess in their vehicles while driving. Let's say if that was the case, then she should be at fault. She's was already driving with a suspended license already.