It is VERY difficult to get a FWD car to oversteer without letting off the throttle. Blackshine, in BOTH those videos you posted, the drivers are letting off the gas to get the rear to slide. In the case of that "drift" Civic, he grabs the ebrake first so that it swings out, and he lets off of the gas. It is also easier to do in that car because of the short wheel base and high spring rates in the rear. If you listen to Jeremy in the second video you posted from Top Gear, at exactly 00:49 seconds into the video Jeremy says "if you turn into a corner without the power on, the back slides around."

You REALLY don't know what you are talking about.

The reason that Type R Civic from the Top Gear video slides when you let off the gas is because of the stiffer rear springs and larger rear sway bar. You can tell it has those stiff rear suspension bits because of the way it lifts the inner wheel in a corner.