nc47,
In your response above, you neglected to point out that the the NAS statement you gave was from
"Science, Evolution, and Creationism" (National Academy of Sciences and Institute of Medicine. © 2008 National Academy of Sciences.) In other words, NAS was responding to creationists and religionists.
If you actually read what was written in the statement, you will find that the portion quoted below says pretty much exactly what I wrote in my post above.
Science and religion are based on different aspects of human experience. In science, explanations must be based on evidence drawn from examining the natural world. Scientifically based observations or experiments that conflict with an explanation eventually must lead to modification or even abandonment of that explanation. Religious faith, in contrast, does not depend only on empirical evidence, is not necessarily modified in the face of conflicting evidence, and typically involves supernatural forces or entities. Because they are not a part of nature, supernatural entities cannot be investigated by science.
The following part of the NAS statement you quoted is a version of the (now discredited)
non-overlapping magisteria (NOMA) argument championed by Stephen J. Gould.
In this sense, science and religion are separate and address aspects of human understanding in different ways. Attempts to pit science and religion against each other create controversy where none needs to exist.
Non-overlappimg magisteria has been pretty much discredited by any number of scientists, including Richard Dawkins, who explains the problems with NOMA. He points out, for example, that religion does not, and cannot, be divorced from scientific matters or the material world.
Richard Dawkins wrote: "It is completely unrealistic to claim, as Gould and many others do, that religion keeps itself away from science's turf, restricting itself to morals and values. A universe with a supernatural presence would be a fundamentally and qualitatively different kind of universe from one without. The difference is, inescapably, a scientific difference. Religions make existence claims, and this means scientific claims."
Dawkins goes on to point out that claiming that these two magisteria do not overlap..." does not consider the claims of many religions upon material reality, such as miracles or prayer."
In other words, if one is going to claim non-overlapping magisteria, as the NAS essentially did in the statement you quoted (which was offered in more of a diplomatic or political context than a scientific one), then one would also have to agree that religion's claims as to creation and miracles, for example, be dropped because they overlap with science. In fact, they constitute falsifiable hypotheses. When these hypotheses are tested scientifically, they are invariably found to be -well- false.
If one is not willing to disavow creationism, miracles, etc. then one must accept that the magisteria of science and religion do, in fact, overlap. Wherever this occurs, the two come in conflict, and when they do science is shown to be the preeminent magisterium - every time.
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ETA:
nc47, just saw that you did provide a link to the NAS statement you quoted, while I was writing this.
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ETA2: Micro-resume deleted in deference to Quasi's post below. 
