These people use their abilities and consider the data and come to particular conclusions about it. Other people who have similar base credentials examine the data and come to quite different conclusions about it. Opposing conclusion in fact.
In the sciences this is always a possible outcome and, in fact, is rather frequent. The process is designed to work through this.
The individuals publish, in very, very great detail their reasoning. Then others critisize it and it is corrected.
Unfortunately, the proponents of ID seem to want to go directly to the public and, at least in what I've seen ignore critism. The mathematical probability arguments still seem to be put forward even though it is pretty easy to show they flaws in them.
Why is that?
Can a closed group of people get it very badly wrong?
Yes, but so far the process has been shown to (slowly perhaps) correct when things are wrong.
You can speculate about such problems all you want. All that really counts is that you show where it has gone wrong. The ID folks don't seem to be doing a great job of that so far.