I found that the ReadReceipt = false had no effect and still got Read Receipts from mail sent to recipients.

The default for ReadReceipt is true and in turn writes the key “Disposition Notification-To” to the mail header.

The workaround I used was to remove the key:

SmtpMail oMail = new SmtpMail("XXXXXXXXXXXXX");
.
.
.
oMail.TextBody = "";
oMail.DeliveryNotification = DeliveryNotificationOptions.None;
oMail.IgnoreDeliveryNotificationError = true;
oMail.Priority = MailPriority.Normal;
oMail.Headers.RemoveAt(27);

No Read Receipt requests popped up when recipients open the email.

Hope it helps although it might be a temporary solution.