The key difference between ID and science in your example is that science actively seeks out and tests alternate causes, ID does not.
ID is not designed to
find an answer--to IDers, the answer is already known. Instead it is designed to
support that answer.
Unfortunately (as you point out) rather than follow the scientific method and test alternate causes they focus on a single cause and ignore, misrepresent, or deny any evidence that points to other causes.
Perhaps the prime example of this is the RATE Project, although this may be considered more a creationist group than an ID group.
The RATE boys set out to test the decay constant. The group included a number of qualified scientists, and they used scientific equipment and tests. What their evidence showed is that the decay constant had been stable for some millions of years at minimum--in other words, scientists were right and their religious beliefs were not supported by the evidence.
They did the only thing a creationist/IDer could do: they ignored the evidence and stuck to their religious belief.
Here are a couple of reviews of the RATE Project that discuss this creation/ID version of the scientific method in more detail:
Assessing the RATE Project: Essay Review by Randy Isaac
Do the RATE Findings Negate Mainstream Science?
Edited by Coyote, : Missed a word
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.