I don't think that's correct? It's probabilistic, yes, but in expectation you would still need ~2^64 hashes to find a collision for a 128-bit hash (birthday paradox).
See my above comment. There's a huge difference between having a collision somewhere in a pile of 2^64 hashes, and actually having the colliding hashes ready to present.
Are you trying to get at the distinction between second preimage and collision resistance? If all you need is a collision, "try random pairs until you find a collision" method works fine and is arbitrarily parallelizable with no storage.
