Respectfully, I believe that this is an untrue statement. On my 4wd and AWD vehicles, traction control includes rear wheel control. The vehicles can cut or increase torque to the back tires through the 4wd or AWD as needed, thereby helping you stop. That torque control is very helpful in keeping the car straight. It is extremely difficult to get my Santa Fe to slip sideways on snow/ice.
Agree 100% to buy the best tires you can afford, and don't let the tread get low.
Ultimately, however, 99% or more of road hazards can be avoided by simply driving a safe speed and maintaining a proper following distance. Throw in basic defensive driving, and assume that people around you will make bad choices, and it becomes darn difficult to get seriously injured in a car wreck. Sure, you'll get your occasional deer or whatnot that pops in front of you, but for everything else, safe driving will keep you out of wrecks better than any tire, braking, or traction control.
Teaching kids to be safe drivers right off the bat is important. I taught each of my kids how to drive. The day I knew that they were ready to go out on their own was when they came to me to complain about how mom tailgated and was generally an unsafe driver who scared them. I'm being completely serious - all of them came to me with that, never having noticed it until I taught them basic safe driving techniques.
Drive like you don't need to rely on ABS and traction control.
And stay off the handset.
Be safe.