I've created a relationship between Email Messages and the Lead object and send/receive emails from the Lead object in Salesforce. The Lead contains a {ref:...} that contains the ID, allowing the service to post a reply to the originating record.
The problem is that I'm the only User that doesn't encounter "Insufficient Privileges" error when attempting to either Read or Reply to the Email Messages.
This holds true regardless of the profile of the other Users (it's been tested with other System Admins), the Status of the incoming email (whether "Replied" or "Read" set as status), or whether or not the other User initially created the Email which is being replied to.
The only thing which sets me apart is that I'm identified as the "Context User" on the Email Service -- but since someone is required to be identified here, I don't believe that this should have an impact.
At this point, I'm at a loss.