After taking a deep breath I came back to the machine in question. Rather than clicking on the form from SP, I started InfoPath and tried to open the from from the application. When doing it this way, I noticed that the "form conflict" message flashed by quickly without allowing the user to decide whether to keep the existing template or get the new one. To allievate this, I removed all of the recently used forms and tried to access the form again. This time all worked the way it was supposed to.