The article was about bicycles and motorcycles, not opposite lock countersteering in a car.
I don't know what exactly you mean by "losing traction" (understeer or oversteer) but your advise does not sound correct to me.
But when you get into an oversteer situation in a car, the aligning moment acting on the tyre contact patch will automatically counter steer the front wheels to the outside corner (assuming the fronts still have grip).
The correct response to oversteer is opposite lock (counter steer) to the outside (not to the inside!) and rapid recovery (center the steering wheel) when the car starts to correct itself. In a front wheel drive car, some throttle can help to correct the oversteer faster but it can also induce a really bad tank slapper pendulum and you shouldn't do this in public roads. In a rear wheel drive, if the reason for the oversteer is too much throttle (power slide), easing off the throttle will correct it. But getting off the throttle quickly (esp if you're not power sliding) can also induce lift-off oversteer and make the oversteer worse.
In an understeer condition, just easing gently off the steering and the throttle will usually correct the situation but doing it too quickly can induce a tank slapper oversteer (from lift off oversteer), which you need to correct by counter steering. It sounds like this is the scenario you're describing, but you should definitely not apply more steering input in this situation.
In a road car you will almost never get to an oversteer without deliberately inducing by power sliding, hand brake, scandi flick or other rally driving moves (or accidentally in the case of a bad recovery from an understeer). Road cars' vehicle dynamics are set up to be very understeering through mass distribution and suspension set up.
My driver's education had two full days of skidpad training in slippery conditions. Opposite lock was the response that they taught for oversteer (which the instructor induced by pulling the hand brake in a turn). I also used to do a lot of parking lot snow drifting back when cars didn't have nanny electronics to prevent it. On top of that I have done lots and lots of simulator racing, both track and rally.