Your "two different reasoning" are a minuscule fraction of the possible ways the AI might make its decision. Here are some other ways:
After $17$ iterations, node $4321$ has weight $0.950293159$, which is within the tolerance to trigger node $92384$, therefore the answer is "cooperate".
The literature in the LLM training set tends toward "defect" $85.03\%$ of the time, so the answer is "defect".
But it seems that what you mean by an "AI" in the question has nothing to do with any actual AI that has ever been built; it is rather a mechanized, deterministic substitute for the "perfect logician" that some puzzles refer to.
This presupposes that the answers are "yes" to all of the following questions:
Is it possible for a "perfect logician" to be mechanized and deterministic?
Is the question one that a deterministic perfect logician can answer?
Is it possible for both prisoners to receive truly identical copies of the same mechanized, deterministic perfect logician in the exact same initial state? [Note: this is probably the easiest of these questions to answer "yes" to, assuming the answer to the previous question is, "Yes, and it can be done with software that is just like the deterministic software programs we know today except that it has different lines of code."]
Is it possible for two "rather stupid people" to be able to pose this question to the AI, including all the information and preferences the AI needs to know about in order to make a decision, in such a way that the AI will actually be answering the desired question, not some completely different question that the users asked due to their incompetence?
If the two "rather stupid people" actually are able to use the AI competently, how can they be sure that they both feed the exact same question (up to differences that make no difference) into the AI?
How does prisoner B know that prisoner A is using the same AI (required in order for prisoner B to tell the AI "that the other decision is determined by the same program.")
A facile response to the question might be that there's no reason to believe that the circumstances posed in the question could ever be realized.
Assuming the answers to the first three questions were all "yes", the problem of how the prisoners ask the question might be addressed by giving each of them a document that they should type into the AI's interface verbatim in order to ask the question -- or better still, a device like a USB key that they simply insert in order to ask the question.
But a simpler solution is to deliver each of them an "AI" that simply prints out "cooperate" no matter what the input is.
To put it another way, in order to solve the various "how do they know how to ask the right question" problems, we need some helpful extra circumstances, such as coordination between the prisoners before they are isolated from each other or the intervention of a friendly third party.
I don't believe the original prisoner's dilemma requires any "hypothesis that the other prisoner will reason slightly differently than us".
It merely requires the lack of a hypothesis that there is some unexplained chain of events that forces the other prisoner to make the same decision I make, no matter what that decision is (or at least do so in the case where I decide "cooperate"). The reasoning of the AI in this question is that chain of events (unexplained, because the question doesn't present a mechanical proof).