The way you worded that it sounds like you were using your own GT-R. You can't. If you were using the Arcade version of the car there would be no reason to check that you had 'no modifications.'
It explicitly states that you must use the Arcade version of the car in the trophy info, yet this is apparently a very common mistake.
If you used the right car and didn't cut, no idea. Bad luck?
By the way: I just tried it once with me wheel and did a quite good lap, but I wonder: how hard can it be? I mean honestely, how hard is it? And if yes, what are your best times?