Maybe I'm missing something, but the phrase doesn't make sense to me. Yet I hear it all the time. "I had a near miss," somebody will say. What they mean, I think, is that something bad almost happened . . . but didn't. And they refer to it as a near miss.
Actually, what they are describing is a near hit. They didn't nearly miss something; they actually missed it. Not to parse the words too closely, but a near miss would be a hit. And a near hit would be a miss.
I realize that it's a fine point, but it's a point that I've been thinking about all day . . . in light of what almost happened last night.
Last night, we had a near hit that, thankfully, turned out to be a miss. Not a near miss, but an honest-to-goodness miss.