Our service does not change the status of the ticket when posting a private comment update or read receipt. A private comment whether posted by My Read Receipts or by one of your agents will cause your triggers to execute. Your trigger settings likely cause this behavior.
In order to diagnose the cause of this please look at your ticket event log for the affected tickets. You will be able to see which triggers are firing. Once you determine which trigger is causing the status change you may add a condition that looks for 'MyReadReceipt' in the private comment update and suppresses that trigger from firing. Another option is to change from private comment based read receipts to custom ticket field/event log read receipts.
If you have any questions, please feel free to contact support.