We've discussed similar things many times here, but I just want to mention that I think maybe you just need more practice with GT5P to be able to "chuck it around a bit". The GT series does *feel* very different than most other racing SIMS, but your experience is exactly the opposite of mine. For me (and I'm a HUGE GT fan, like most people here), GT5P currently feels way too easy for me to chuck the cars about and then catch them. I'm running with a G25, so of course your experience may be different.
One key difference between GT and other SIMS appears to be that GT (at least GT4 and 5P) simulates (in force-feedback) the weight-balance of a car much better. But it also completely skips modeling the understeer through the force-feedback. This can be very confusing to those of us who play other SIMS or who do amateur motorsports. For example, in my classic RR Porsche, I can feel the understeer build very clearly though the steering wheel. I know at any time how much grip I have left at the front end. My classic VW Beetle does the same thing, but of course does it much less grace than the Porsche. As I go faster and begin to understeer, the wheel lightens, as I let-off the gas and allow the front to settle, the steering wheel weights-up. Most racing SIMS I've played model this through force-feedback. GT4 and GT5P don't model this at all as far as I can tell. You are completely reliant upon visual information to tell when you are losing front-end grip. For this reason, even though I LOVE the GT series, I'll never be as comfortable driving it as I will other SIMS. I have to go slower into almost every corner than I would like because I just can't tell with accuracy how much front-end grip I've still go available to me - part of the necessary feedback just isn't there. On the other hand, the way it models the weight-balance of a car (I'm a big RR fan) is better, by far, than any other SIM I've played. Feels very "true to life" (even a bit exaggerated, but that's fine considering that you're missing all other G-forces). If you are used to other SIMS, you may find it is the lack of understeer feedback which is causing your problems in GT5P. It may simply be that the motors in FFB wheels can't model everything at the same time, and Polyphony has chosen to model weight balance as a priority and thus can't use the motors to model understeer.
And a big thanks for posting that video! I've never seen such a clear comparison of driving styles. I'm definitely the third type (I like the rear to steer the car). But, I have to say that in many cases the first type (smooth) is going to be an advantage. I almost always run some "fast laps" and some "fun laps". Smoother is faster. I just got done doing two weekends of Ice-X (autocross on frozen lakes), (took a 2nd place and two 1st place trophies in the rear-wheel-drive classification, thank you very much!). My fun drifting laps were as much as 10 seconds slower than my "smooth but fast" laps. So those F1 drivers who are chucking the car about are obviously extremely talented, but the laws of physics suggest that if they learned to be smooth they would be even faster.
Dude, that was long.