Also, in the case of someone running a stop sign, it is far from a sure bet they are going to hit their brakes at all, so by swerving you increase the odds that you will still hit them, but now it will be while you have exhausted all your adhesion on lateral control. So now instead of a front end collision with all the benefits of airbags and crumple zones, you are at a significant risk of rolling the car or spinning off the road and hitting something immovable with a part of your car lacking crumple zones.

Nobody killed, according to the news, but several taken to hospital in critical condition.

Oh, I say unscathed but our tyre exploded the next day, as apparently we caught a fragment, and again, that’s not a “slam on the brakes” moment, but rather “trundle to a stop on the shoulder and walk to the conveniently nearby tyre shop”.

So, the correct advice is to say "brake, don't swerve", so that drivers internalize that their first thought and reaction in any emergency should be to brake. Teach them to actually brake—fully press on the pedal—while you're at it.

A slightly more nuanced advice would be "brake first, swerve as needed as a follow-up".

But I would never in good conscience be able to give anyone advice to swerve instead of braking.