The Verdict Without the Trial
A right answer, carried to a new car. Use it yourself.

“I thought letting go was the same as giving up.”
Some answers arrive finished, without the reasons they were true for.
Here is one.
On ice, pump the brakes.
so the wheels don’t lock and slide
An older car, on ice. Brake lights ahead.
Under the surface
The condition the answer carried. Pumping the brakes on a slippery road keeps the wheels from locking, so the tires keep their grip and the car can still be steered. That advice was right for brakes that lock. Anti-lock brakes do the pumping themselves, many times a second; with them, the guidance is to press firmly, hold, and steer. The sentence stayed the same. What it depended on changed.
Why this happens to answers in general. An answer is usually kept without the conditions it was true under, or the reasoning that got there. Taught as a finished rule, it can't tell you when it has stopped applying. The same is true of procedures, of policies, and of systems that store solutions without the situations they solved. An answer that travels with its reasons can be checked against a new case; one without them can only be repeated.
What the scene simplifies. Real stopping distances depend on the road, the tires and the speed; anti-lock brakes are mostly about keeping the car steerable while braking hard, not always about stopping shorter. Some older trucks and vans have anti-lock brakes on the rear wheels only, where the old advice can still apply. The scene keeps one thing exact: with brakes that already pulse themselves, pumping the pedal works against them and can reduce their effect. How much, and whether it costs distance or steering, depends on the conditions; the scene shows one road where it costs distance.
Source. U.S. National Highway Traffic Safety Administration, consumer guidance on anti-lock brakes (1996): keep firm pressure on the pedal and do not pump it, or "you will defeat the purpose of the ABS or reduce the effectiveness of the brakes."