To reproduce:
- Add RadDateTimePicker to a form and set its ReadOnly property to true.
- Paste a valid value using the Ctrl+V key combination.

Workaround:
- Disable the corresponding key combination in the KeyDown event:

void radDateTimePicker1_KeyDown(object sender, KeyEventArgs e)
{
    if (e.Control && e.KeyCode == Keys.V)
    {
        e.SuppressKeyPress = true;
    }
}