My understanding of it:
If you've got higher grip tyres, the car's handling and braking are more effective, and the car is able to generate higher forces while doing both.
Grippier-Tyres-Does-Improve-Braking Lecture
It's true that, in swapping for higher-grip tyres, you've not actually modified the brakes, but they are still effective for the reason that every single braking system on a car (with perhaps .01% exceptions in certain cars) is overkill; the only thing ever keeping the wheels from locking up under braking is ABS, which detects when the wheels are about to lock up, and releases some brake pressure. Applying grippier tyres means that the tyres are less prone to lock-up, and the brakes can be applied further and more intensely, and the braking improves.
Here's an experiment: Buy a Mitsubishi FTO, and test its behaviour under trail-braking first with S2 tyres, then with R3 tyres. With the S2 tyres, there is a moderate-to-high amount of forward weight transfer, and the forward weight transfer pushes the front tyres harder into the road while subtly lifting the rear tyres, giving the rear less traction than the front, allowing momentary oversteer in smallish doses. If you try the same thing with R3 tyres, the resultant huge braking force hurls the car forward, practically lifting the rear tyres, and giving you a possible huge, 70-degree-angle drift before the effective tyres grip the road again, and you exit the corner with full grip regained.
The same effect is at work in the muscle car, where higher-grip tyres yield driftability due to braking-weight-transfer. However, a muscle car, unlike the FTO I mentioned above, is a heavy car with lots of momentum, the momentum meaning that it has the ability to overcome the grippy tyres wanting to regrip mid-turn. Also, since it's a slow-to-respond muscle car, you won't be wrangling lightining-fast reflexes when using grippy tyres, so the slower reflexes mean the car is easier to control and thus drifting is easier.
In other words, the grippy tyres allow forward weight transfer under braking, which allows the rear to swing out, then the muscle cars' heavy, unresponsive handling allows the drift to plow onward, the weight overwhelming the tyres, and the unresponsiveness allowing much room for driver error. Actually, I found that my Mercury Cougar drifted much more easily on S2 tyres than any N-tyre I tried on it.
For these reasons, muscle cars in GT4 are actually brilliant at drifting in their own special way. All cars endure the weight transfer under braking, but if you try the same trick in a responsive car, you'll find every slight error in your driving hugely magnified through the huge grip. So you put grippy tyres on ungrippy cars, and ungrippy tyres on grippy cars. All this leads to my elegant conclusion regarding GT4 Drifting Tyre choice:
Equip your car with tyres just slippery enough to be able to controllably maintain drift without risking snapback, because uneffective tyres have trouble initiating drift.
