I think it is fair to say that most ECs say that God’s intervention/guidance/intelligence is not detectable in nature with the tools of science. Somehow the fact that science precludes describing supernatural involvement always seems to get conflated with “ECs think only natural explanations are needed/allowed to describe all of reality.”
You can see in the discussion with Daniel here that somehow the fact that ECs are not “open to pursuing non-natural explanations through science” is this big deal, and it doesn’t seem to make sense to them when you say, science can’t pursue non-natural explanations. That’s a premise not a conclusion. It’s not that we have concluded that “divine intervention not only can’t be detected, but indeed has not occurred,” it’s just a premise going into any scientific investigation that you will be seeking natural explanations.
I think people assume that EC is a scientific model. So they have a hard time grasping the fact that the evolutionary part of the perspective only deals with “natural explanations” and the creationism part of perspective is arrived at by other ways of knowing.