Is it a low grumble or more like a thump thump thump?
The thumping is kind of what they are describing but its not purely because the tyres are too wide. When you turn the wheels of the car to full lock, the camber of the wheel changes such that it tilts the wheels over to extreme angles and decreases the contact patch on the road. This means the car will scrabble for grip, jumping from having grip, to no grip, to finding it again. Its a nasty sensation and completely normal in the 370z. Its because the car has big front tyres and also because they wanted to keep the turning circle smaller, and in this country with cold weather (less maluable tyres), it scrabbles on full lock. When going faster, the inertia will push the weight to the outside and correct this angle and so contact patch is right again, but slow speeds it doesnt have the weight on the contact patch.
Go outside and stick the car on full lock and look at the tyres, you'll see what I mean