Well, MSDN is right. That is what the Caption
property is for. However, that doesn't mean that control makers have to use the caption property. In this case, Microsoft didn't do that (although they really should have). You can modify your code to this though:
///snip
dataGridView1.DataSource = dt;
foreach (DataGridViewColumn col in dataGridView1.Columns) {
col.HeaderText = dt.Columns[col.HeaderText].Caption;
}