The lowercase ‘id’ is to distinguish it from the ID movement as exemplified by Michael Behe, The Discovery Institute, evolutionnews.org and bio-complexity.org/.
I agree that confessing scientists here believe that design cannot be detected by science. That God’s role can be detected by science is not how I would characterize atheists’ view. Rather, they think if God were active in his creation, his activity should be detectable and must have scientifically detectable evidence in order for them to believe that God exists.
I would welcome any way that ID folks could come up with that could definitively demonstrate God’s design scientifically, and Winston Ewert has admirably tried (and been addressed here, as well).
But scientific demonstration of God’s activity might actually be counter to his purposes (that seems counterintuitive, speaking of counter 
). After all, he wants us to have faith, and scientific proof would constitute compulsion. That has been discussed here before, too (and here). So maybe I shouldn’t hope for scientific demonstration of design after all, even though it might be personally gratifying to me as a Christian. And maybe, for the aforementioned reason and as confessing scientists here believe, pursuit of it is futile, and not the best use of ID movement leaders’ and supporters’ resources.
I do think that the fact that there is design is intuitive though, and rightfully so, just not that we can prove that it is a fact, as already noted.