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Just by exploring checkboxInputBinding input binding we can confirm that shiny is using type = "checkbox" in the input tag.

var checkboxInputBinding = new InputBinding();
$.extend(checkboxInputBinding, {
  find: function(scope) {
    return $(scope).find('input[type="checkbox"]');
  },
// ....; Extra code removed
  }
});

inputBindings.register(checkboxInputBinding, 'shiny.checkboxInput');