I fully agree with you that it is not open to private interpretation. To me, that means that we must not look at the Bible in the way that we like best, or in the way that we feel we have to. We have a responisibility to try to find the intended meaning of the author.
And yes, that does mean that it's open to interpretation. You cannot look at a 2000+ year old book an know exactly what the authors meant. We have to remember that the authors lived vastly different lives from each other, thought differently from each other, and lived and thought differently from us. This means that different parts of the Bible must be read differently.
So, while we must not look for selfish interpretations, we must always been on quest to find the most correct ones. We may never find out exactly what some passages mean or we may disagree on it, and it is important to understand that.
I could be wrong about how I interpret Genesis and other books. You might be wrong too, SackLunch. We all could be.
The thing is, "no private interpretations" does not mean "no interpretations period." When you read the works of any author, listen to any song, look at any work of art, you interpret it. You look at the clues left by the author, songwriter, or artist to discern what it means. If the author is still alive today, sometimes we can just ask them what they meant. But none of the authors of the Bible are alive. We cannot get inside their heads. The best we can do is look the clues left behind by their cultures to find how it would apply to them and to us today. That's why we come up with different ideas. We're not all detectives and we might not know exactly how to read the clues.
That is the best we can do, and that is an honest way to interpret. Look for what you believe the passage was originally supposed to mean, not what you want it to mean or what everyone tells you its supposed to mean. That, I believe, is what Paul was commanding us to do.
I feel that you wrote this post with the idea that your way of reading the Bible is the right way. If that is not true, please correct me. You must understand that the TEs are not privately interpreting the Bible. That's just where the clues lead us. We're prepared to admit we might make mistakes about reading it (at least, I am) as we learn more about the ancient peoples. I hope you are also prepared to learn the same.