[swampangel]

I think this expression would be familiar to most native English speakers, but it is idiomatic.

It's using "near" as a synonym to "close" -- as in "a close shave" (actually close) rather than as a synonym for "close to" as it is in the expression "near death" (almost, but not quite dead).

The second sense is definitely more common.

This post suggests "near miss" became common as a military phrase to mean "missed, but still damaged the target" but changed as it entered the vernacular:

http://www.worldwidewords.org/qa/qa-nea1.htm