React.js table: remove row button visually removes incorrect row

I am using React.js to dynamically create a html table containing text boxes. I have rows that can be removed by a button click. I expect, when I click "remove" on the first row that the table re-renders with row 1 removed. However, when react re-draws the table, it looks like it always removes the last row of the table from the DOM instead of using the actual values from my state object. Perhaps I found a bug? Here's my code:

/** @jsx React.DOM */

var MyApp = React.createClass({
    getInitialState: function () {
      return {
        col_one: ['c1r1', 'c1r2', 'c1r3'],
        col_two: ['c2r1', 'c1r2', 'c1r3'],
        col_three: ['c3r1', 'c3r2', 'c3r3']
      }
    },
    handleCellChange: function (colName, index, e) {
      console.log('onChange:', colName, index, e.target.value);
    },
    handleRemove: function (i) {
      var that = this;
      console.log('removing row:',i);
      _.forEach(this.state, function (val, colName) {
        that.state[colName].splice(i,1); // BUG???
        //_.pullAt(that.state[key], i); // doesn't work either
      });
      console.log(this.state);
      this.setState(this.state);

    },
    render: function() {
      var that = this,
        rows = [],
        cols = _.keys(this.state);

      rows.push(
      <tr>
      {cols.map(function (col) {
        return (
          <th>{col}</th>
        )
      })}
      </tr>
      )
      for (var i = 0; i < this.state[cols[0]].length; i++) {
        rows.push(
          <tr>
            {cols.map(function (col) {
              return (
                <td>
                  <input type="text" defaultValue={that.state[col][i]} onChange={that.handleCellChange.bind(that, col, i)} />
                </td>
              )
            })}
            <td>
              <button onClick={this.handleRemove.bind(this, i)}>Remove</button>
            </td>
          </tr>
        )
      }

      return (
        <table>
          <tbody>
            {rows}
          </tbody>
        </table>
      );
    }
});

React.renderComponent(<MyApp />, document.body);

seen here as a JSBin