If you look at the thread I linked in an earlier message, FoughtFyr, goes from a 2.8 or something uGPA to a 3.8MPH and gets in. He (I think he, but not sure) claims the MPH was brought up at nearly every interview, and mentioned as a plus. He also served on an adcom as well later on. He has a pretty amazing app, not counting the uGPa. But there's no way his MPH was useless.
What is more, others posters that thread who got an MS and went to med school said that few students with an MS were turned down, and that MS is seen very differently than an MPH.
I mean, there are 120-some med school, not counting the DOs, so I really can't think all of them look upon grad school as a 'really good EC', especially when you consider what some of the posters in that other thread said.
Please consult a dictionary on your use of a priori.
Eh, I don't think anyone here said that a master's degree would be, in your words, "useless." On the contrary. Anything you do that distinguishes you is of benefit in this process. I think by that reasoning, a master's degree would be looked upon favorably by any adcom, more or less depending on the given school in question. However, in general, you can't readily expect that a master's degree will compensate for a poor UGPA and/or a poor MCAT, if that is indeed the issue. Of course, if you look around, you'll definitely find exceptions. People have gotten in with quite a range of different UGPA and MCAT scores, I'm sure, even without a master's. It's such a variable process and there are so many different factors involved, that it's very hard to nail down that one thing that got you accepted; we can only guess, most of the time, and we'd do well to guess that it was a multitude of factors, including plain old luck. Nevertheless, there are schools that screen based on UGPA and MCAT, and it's quite clear that these specific statistics are what most medical schools value. This has been hammered in me by now through a variety of sources. Does this mean that you absolutely HAVE to raise that UGPA to get accepted and that some other method, such as completing an MPH won't work? Nope, not at all, especially if you've already worked the post-baccalaureate undergraduate class route to death already. But assuming you haven't beaten that route to death, raising that UGPA significantly and trending A's in advanced undergraduate science classes is definitely high yield in this process, and it will more than likely help you in most, if not in all, cases, if that is what is lacking on an otherwise good application. It's the conventional path, and it is known to work. But, hey, if you want to get that MPH, or another master's degree, and you are highly determined, I'm sure you can get it to work for you. I've learned to be cautious about saying never. There's certainly no accounting for the power of the human spirit and what we can accomplish in any given situation. As I've heard it once said, "there are many paths, but one mountain." There's no one formula for getting accepted, and I'm not going to stand here claiming that there is any best way. I just know what I've heard time and time again from many people. Could I be mistaken? Absolutely. The way I see it, do what you most want to do, take in all the useful feedback, trust your educated intuition on what is best for you, and if you do it smartly, I'm sure you can make it work.
Now that I think of it, after writing that tome above in response to your post, the best advice I can give is to talk to the medical schools in which you are interested in applying and ask them DIRECTLY what will most improve your application and exactly how to do it. Yeah, now that's getting it down to laser-point accuracy and precision; what better source than right from the horse's mouth.