I'm not well-versed in this, but I think you're wrong. A MD5 hash has 2^128 permutations, so it's like the birthday problem, you'll get 50% chance of any two files in a set having the same hash with far fewer than 2^64 files.

Besides, we're talking about probabilities. It's possible for 2 files, one after the other, to have the exact same hash just because of chance. In fact, I think there was a bitcoin bug due to this, something about making the wrong assumption that the hash of the entire blockchain and the hash of the entire blockchain + 1 block would never be the same hash, if I remember correctly.

Hashes are simply not a reliable method of uniquely identifying things. They are a convenient method but if you implement any hash-based system for identification you should also implement a escape hatch for when two different things have the same hash but must be treated differently.