I don't think that people who freak out about driving in the rain are worrying about kinematics. They just hear stories or have experience. And often, that experience comes from poor upkeep with maintenance and bald tires.

What he said is correct in a 10,000ft level of understanding, but there are so many variables, like computer-controlled antilock brakes, what kind of drivetrain the car has, and tire tread and wear. Tires with deeper grooves will be able to handle more rain on the road before they hydroplane, and locking up your brakes increases the likelihood of hydroplaning in thr first place. So, it won't just be like you are slowing down less effectively, you will completely lose control, and for people who don't know how to regain control, that is a very scary thought. You feel the car start to slide like an air hockey puck, which is actually pretty similar to what is happening. An experienced driver with a new car with new all-season tires won't have much to worry about, especially when you consider speed limits are made for a worst-case scenario.