"Near miss" is a correct term to describe something that comes close to hitting something else. I hate it when people say that "near miss" would really be a collision. The most common meaning of near means close, usually in space. If I am shooting at a target and I got close to it but didn't quite hit it, that would both be a miss and it would be near the target, therefore it would be a "near miss". If I had missed way off to the side, it would be a "far miss". You could say "The miss was near the target", so why can't you call it a "near miss"?
If you have a low ceiling you might say "The ceiling is near". You could say it was a "near ceiling". It would be a stretch to interpret this as meaning "It is almost a ceiling, but not quite."
Why do so many pedants skip to the fifth definition when complaining about this term?