I disagree. The word 'miss' does not tell you how close it was. If I kick a ball at 90 degrees to the goal post, then I have "missed by a mile". If it just whizzes by the wrong side of the post, then it is a 'near' miss. I think that an adjective is OK in that context. In some cases it is important to know how close it was, like when a torpedo is aimed at your boat, a near miss is more dramatic.
A tautology is only such if the adjective or adverb is already implied in the noun or verb that is being modified. Free gift is a tautology, as is pierced through. Near miss is not.
It's not an oxymoron either because near does not contradict miss.
People say "miss hit", when they mean someone hit the ball incorrectly, and on the face of it that is an oxymoron. But miss is used in the sense of misfit or mismatch, rather than miss vs hit. Same source probably.