Do you maintain that The Design Inference is a treatise on theology? (I'm assuming that you've actually read and understood what you are characterizing.)
Becoming a Disciplined Science: Prospects, Pitfalls, and a Reality Check for ID
A Dembski man! I think you mean this book.
This book presents a reliable method for detecting intelligent causes: the design inference. The design inference uncovers intelligent causes by isolating the key trademark of intelligent causes: specified events of small probability. Design inferences can be found in a range of scientific pursuits from forensic science to research into the origins of life to the search for extraterrestrial intelligence. This challenging and provocative book shows how incomplete undirected causes are for science and breathes new life into classical design arguments.
Yes. I maintain this is just another attempt to impose theology on science. It's reasoning from analogy and bad mathematics to make a case for the obviously existent designer. (He doesn't explain why the designer makes more extinct species than living ones.)
It reads more like Biblical Scholarship rather than a science.