I also can't show conclusive evidence that there wasn't a continent of Atlantis in the middle of the Atlantic 10k years ago that mysteriously disappeared without a trace. Yet if someone enters a conversation about geography with me and inquiries about Atlantis I'm probably going to tell them that it never existed without bothering to wrap that statement in multiple layers of clarification about the evidence and probability estimates and highly unlikely contingencies.
We can't prove that there wasn't some isolated genius who engaged in animal husbandry in Africa before everyone else but was ignored by the rest of his tribe or whatever. But we have managed to place some fairly low upper bound on how much of that could have been happening. At some point it is reasonable to conclude that your typical society in that time and place didn't have access to it.
Well sure a very slim chance is a reasonable position.
Not in the way that people usually use those words. "Reasonable position" generally refers to a reasonable assumption to make or gamble to take. Something technically remaining within the realm of possibility is not that.
And your personal opinion on this alleged standard is relevant because…?
Edit: clarified the question
Because the two of us appear to be attempting to communicate and effective use of language requires some level of mutual understanding of vocabulary. The statement you made does not hold when those words are taken to mean what I broadly understand them to mean.
Which is to say that no, a very slim chance is not a reasonable position to take in most contexts.