make change after vector::at returns a reference

#include <iostream>
#include <vector>
using namespace std;
int main() {
  vector<int> nums {0,1,2};
  vector<int> copy {0};
  copy.at(0) = nums.at(0);  // nums.at(0) returns a reference
  nums.at(0) = -1;          // why this line doesn't change copy[0]

  std::cout << copy.at(0);  // print 0
}

Hi, as code indicates, it looks like changing of nums.at(0) doesn't affect nums.at(0). Does copy.at(0) = nums.at(0); call the copy-assignment operator a copy? It doesn't make sense to me this line actually do a copy, because copy.at(0) also returns a reference.