The map of US rainforests shows an active rainforest along the western side of North Carolina. It is not all that hard to believe said forest could have been much larger before the human touch.
The easternly side of the forest to the easternmost points of NC is not further than LA from SF, though. Unless you live way out in the ocean, but still consider that to be North Carolina for some reason, you are closer than said distance to the forest.
I do I. Fact live almost at the Coast. Just to get to Asheville, which is hardly the westernmost point in the state, is over 6 hours.
Los Angeles to SF is 381 miles.
My town to the Cherokee, which is about where the rainforest zone starts, is 383. North Carolina is a much bigger state than most people realize.
Nobody has ever thought North Carolina was small, though. Where did that idea come from? In fact, it is not clear why the record needed a distance in the first place.
I assure you, as life long resident, I have blown the minds of many non-natives by stating I can drive for 8 hours west and still not quite be in Tennessee. In most places east of the Mississippi that gets you through 3-4 states.
It's all relative, I guess. I'm looking at 20 hours of driving to get the western extent of the province. And seven hours the other way to get to the easternmost side. 8 hours is but a leisurely afternoon cruise.
I don't know much about NC, but the only parrot native to the US used to live there [0], which indicates that it must have been pretty heavily forested prior to the Colombian exchange.