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");
.
.
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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.