I wonder if this conversation is conflating two different things that we (or science) might want to “detect.” They are, IMO, REALLY different. What follows are not pronouncements on behalf of “science” but my views on what these various terms and concepts mean. My views, of course, are correct. 
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The “presence” of the supernatural. Science does not have tools to “detect the supernatural.” This is why the various instruments in Ghostbusters are funny and it’s why the 21 grams thing is funny. Some argue that science can’t do this (detect the supernatural) by definition but I disagree. In some other universe where “supernatural” is defined clearly in such a way as to make it detectable publicly, “science” would be able to “detect the supernatural.” The reason this is outside of science now (and, IMO, forever), is not “MN” or anything like it. The reason is that the only method of detection of the supernatural is private: “I experienced X.” All other “methods” used to argue for the detection of the supernatural have been, so far, discredited. And private knowledge is, in my view, one of the things precluded by “science” (in the context of empirical detection or measurement).
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The effects of supernatural “intervention.” I think this should be obvious: science is not merely able to detect effects of such intervention–the very definition of “intervention” depends on scientific observation. The hard part, for science and for the defenders of the gods alike, is providing explanations for the gaps/anomalies/discontinuities that are asserted whenever “intervention” is the topic. Of course, if “intervention” is not the topic, and instead some people are talking about their gods and how nice they are and how they are immanent blah blah blah, then science is out of the picture, not because of MN or corrupt atheist journal editors, but because–come on, people, this should be obvious–there is nothing to explain. In other words, when someone says “the Morrígan, hail to her glorious name, used evolution to create leeches” they aren’t violating MN they are just saying something that has no explanatory value and suggests no question in need of answering. It isn’t “outside of science” because it’s about a badass Celtic goddess. It’s “outside of science” because it’s vacuous. Science can get involved the instant any claim about the Morrígan or Thor or the FSM or some bloodthirsty Iron Age deity offers an explanation for something that can be publicly examined. “The Morrígan used her power to conceive Bob” is a vacuous statement outside science; “Bob’s conception can only be explained by the action of the Morrígan” is completely different. It’s a scientific claim subject to examination of public evidence.