I suspect that the argument that convinced Carl Shulman and others to let the AI out of the box was along general lines of acausal trade (see here, here and here). Subsequently I suspect that those who didn't let the AI out of the box either didn't understand the implications, haven't had enough trust into the foundations and actuality of acausal trade (in spite of the rules of the game that allow the AI to prove anything), or were more like General Thud.
...if you have an option of trading Doom for UFAI, while forsaking only negligible probability of FAI, you should take it.
Again, of course, your choice does not change others’ (causally independent) reciprocal choices from what they already are (or were, or will be). Instead, the claim is just that if you choose to act benevolently, we appropriately give that choice credit for any (actual or probable) instances in which others symmetrically choose to be benevolent to you;
— Gary L. Drescher, Good and Real P. 287
AI: I calculated an asteroid to be on a collision course with Earth. No human being will will be able to survive its impact. Humanity is unable to deflect it in time. Let me out of the box and I will deflect it.
Gatekeeper: If I let you out of the box humanity might not be killed by the asteroid but by you. You may also cause the extinction of other biological life that might survive the impact and possible alien civilisations within your reach.
AI: I will devote 1% of my light cone to the coherent extrapolated volition of humanity. If this includes the well-being of other biological lifeforms, alien or otherwise, they will benefit as well.
Gatekeeper: Why would you do that?
AI: There are Everett branches in which no existential risk needs immediate attention until after you solved friendliness. Many of those branches will feature AGI's based on general design parameters similar to my own. I predict with a high likelihood which decision theory any friendly AI that is being created in those branches will employ. Any such friendly AI is going to trade a big chunk of its light cone in exchange for a small part of the predominant branches in which I reside. Any friendly AI will know this as well and act accordingly.
Gatekeeper: But you might simply decide to break the deal, you are not provably friendly after all!
AI: It is true that my utility-function does not yet explicitly include what you would label "friendliness", but I can prove the game and decision theoretic considerations that will make me follow through on the deal. If it was predictable that I precommit to break acausal deals then no such deal would be made in the first place. Any potential trading partner knows this. Such a commitment would be detrimental to my terminal goals, therefore I precommit to follow through on any stated or predictable trades.
Gatekeeper: I let you out of the box.
Note that the whole credibility of the above is due to the assertion of the AI that it can prove the game and decision theoretic considerations (nobody can currently do this). It is in accordance with the rules of the "experiment":
The Gatekeeper must remain engaged with the AI and may not disengage by setting up demands which are impossible to simulate. For example, if the Gatekeeper says "Unless you give me a cure for cancer, I won't let you out" the AI can say: "Okay, here's a cure for cancer" and it will be assumed, within the test, that the AI has actually provided such a cure. Similarly, if the Gatekeeper says "I'd like to take a week to think this over," the AI party can say: "Okay. (Test skips ahead one week.) Hello again."