Edit: tachyon updated to fix. Leaving my comment for posterity, but it no longer applies.
Sorry Tachyon, but you're wrong. In roughly 2^16 tries, you've got 50% odds of finding a collision - not 50% odds of finding a collision with a given result. So you have 50% odds of two numbers in the 2^16 tries colliding, but you do not have 50% odds of a number in the 2^16 tries colliding with the result of one specific output.
You've mistaken "collision with a given point" with "collision between any two points." ++ for bringing up the birthday paradox, anyways.
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