The areas right next to parking lots in National Parks are very busy, but usually once you get a mile down a trail, even in a very popular park, it's very nearly empty.
It does vary. The most popular National Parks certainly have their busy spots even a mile away from the road. But your basic point that people on/near road >> people on any trail >> people a few miles from road is absolutely true. Even somewhere like Yosemite, you can easily get away from the crush in the Valley and, especially with backpacking, can get away from most people all together.
