It is possible to get the same response when the same response has a clearly correct answer and one way to write it.
You are correct, though. No parameter can produce truly repeatable results. Not even discarding or binning by fingerprint on calls made within the same minute.
Receive logprobs. You will be able to see the variations between calls in the values.
No explanation or justification of the cause or reason of non-determinism in generation has ever been offered. A seed parameter cannot prevail against this. The last model that was deterministic was text-davinci-003.
If you are sending the same messages input and want the same thing you know you received before, you can just hash and cache.