How does the toggle button work with checkboxes?

I'm referring to the Toggle buttons with checkboxes which I don't understand. There we have the example (I have added some ids):

<div class="btn-group" data-toggle="buttons">
  <label class="btn btn-primary active">
    <input id="c1" type="checkbox" autocomplete="off" checked> Checkbox 1 (pre-checked)
  </label>
  <label class="btn btn-primary">
    <input id="c2" type="checkbox" autocomplete="off"> Checkbox 2
  </label>
  <label class="btn btn-primary">
    <input id="c3" type="checkbox" autocomplete="off"> Checkbox 3
  </label>
</div>

I can click on the third button or use $('#c3').closest('.btn').button('toggle') to set the third button as pressed. That is visually okay. However, the checkbox input does not get the checked attribute, and that is what I'm missing. Why doesn't this happen automatically? Am I required to do this manually?