My example was meant to highlight the principle and it stands because it's a simple straight-forward example that covers almost all if not all the cases. The burden of proof stands with the party making the claim.
You're free to believe an unsubstantiated theory but you can't expect others to prove it wrong in order to make their point.
Now coming back to your hypothesis, it's too complex and contains way too little data to assist in a decision. A random answer would be just as good and proves nothing. I would probably consider performing the experiment on another planet. Or even on this one. Or wait a little longer (which is equivalent to not doing it). What I would definitely not do is say "The premise of your entire [theory] seems to rely on this one fallacy" [approximate quote from OP]. It's only a fallacy after you prove it.
P.S. Is experiment Alpha the detonation of a thermonuclear bomb that might set the atmosphere on fire? Because we know how that decision went :).
I guess my point is who carries the burden is irrelevant if you have to make a decision based on your state of knowledge.
You have a decision to make, and Bob makes a claim which could influence that decision.
Does it matter where the burden lies? You have to make the decision, and Bob has presented new information but doesn't well substantiate it.
My point is this: From a pure reason standpoint, I think it's fair to always assume the negative when there is not evidence for a positive claim. But in the real world where you have to achieve real goals based on partial knowledge, reason would dictate that you sometimes evaluate and consider claims that are not yet well substantiated, and you might have to do the legwork to substantiate the claim yourself (if you decide there is enough merit and value in doing that substantiation).
My point is the burden of proof is, practically, often on the person who needs to make a decision based on information and not on the person who makes a claim with related information.
---
For Alpha, I didn't have something specific in mind but some kind of combination of "light the atmosphere on fire" and more crackpot "your particle accelerator will create a black-hole" were definitely both in the back of my mind.
You're free to believe an unsubstantiated theory but you can't expect others to prove it wrong in order to make their point.
Now coming back to your hypothesis, it's too complex and contains way too little data to assist in a decision. A random answer would be just as good and proves nothing. I would probably consider performing the experiment on another planet. Or even on this one. Or wait a little longer (which is equivalent to not doing it). What I would definitely not do is say "The premise of your entire [theory] seems to rely on this one fallacy" [approximate quote from OP]. It's only a fallacy after you prove it.
P.S. Is experiment Alpha the detonation of a thermonuclear bomb that might set the atmosphere on fire? Because we know how that decision went :).