Why can't I change objects in a vector?

I have a class TileGrid that holds an std::vector< std::vector<Tile> >. Accessing the Tile objects in the vector works, but I can't change their properties? For the sake of completion, here are all the relevant classes:

tilegrid.h

#include <vector>
#include "tile.h"

class TileGrid {

public:
  TileGrid();
  TileGrid(unsigned int rows, unsigned int cols);
  virtual ~TileGrid();
  unsigned int getRows() const { return rows_; };
  unsigned int getCols() const { return cols_; };
  Tile atIndex(unsigned int row, unsigned int col) const { return tiles_[row].at(col); };

private:
  std::vector< std::vector<Tile> > tiles_;
  unsigned int rows_;
  unsigned int cols_;

};

tilegrid.cpp

#include "tilegrid.h"

TileGrid::TileGrid() : rows_(0), cols_(0) {
}

TileGrid::TileGrid(unsigned int rows, unsigned int cols) : rows_(rows), cols_(cols) {
  tiles_.clear();
  for (unsigned int y = 0; y < rows_; y++) {
    std::vector<Tile> horizontalTiles;
    for (unsigned int x = 0; x < cols_; x++) {
      horizontalTiles.push_back(Tile());
    }
    tiles_.push_back(horizontalTiles);
  }
}

TileGrid::~TileGrid() {
}

tile.h

class Tile {

public:
  Tile();
  virtual ~Tile();
  bool isActive() const { return isActive_; };
  void setActive(bool status) { isActive_ = status; };

private:
  bool isActive_;

};

tile.cpp

#include "tile.h"

Tile::Tile() : isActive_(false) {
}

Tile::~Tile() {
}

main.cpp

#include "tilegrid.h"
#include <iostream>

int main() {

  TileGrid tg(20, 20);

  for (unsigned int i = 0; i < tg.getRows(); i++) {
    for (unsigned int j = 0; j < tg.getCols(); j++) {
      if (tg.atIndex(i, j).isActive()) {
        std::cout << i << "," << j << " is active" << std::endl;
      } else {
        std::cout << i << "," << j << " is NOT active" << std::endl;
      }
    }
  }

  // This is all working. But when I for example use the setActive function, nothing changes:

  tg.atIndex(1, 0).setActive(true);

  // When I print it again, the values are still the ones that were set in the constructor

  for (unsigned int i = 0; i < tg.getRows(); i++) {
    for (unsigned int j = 0; j < tg.getCols(); j++) {
      if (tg.atIndex(i, j).isActive()) {
        std::cout << i << "," << j << " is active" << std::endl;
      } else {
        std::cout << i << "," << j << " is NOT active" << std::endl;
      }
    }
  }

  return 0;

}

I'm really sorry for all this code... I tried to keep it as short as possible, but I thought it'd be better to post it all!

So yeah, my problem is the setActive function. When I just create a Tile and call its setActive function, everything works, but when I call it through the TileGrid object, it won't.

I have tried to solve this on my own for hours and I can't think straight anymore. I'm really desperate here, could you please have a look and maybe help me?