You can get the same output from different mechanisms, like in your example. Another would be that it's equally possible to quickly do addition on a modern pocket calculator and an arithmometer, despite them fundamentally being different. However.
1. You can infer the output from the mechanism. (Because it is implemented by it).
2. You can't infer the mechanism from the output. (Because different mechanisms can easily produce the same output).
My point here is 1, in response to the parent commenter's "the mechanism of operation dictates the output, which isn't necessarily true". The mechanism of operation (whether of LLMs or sunflowers) absolutely dictates their output, and we can make valid inferences about that output based on how we understand that mechanism operates.
1. You can infer the output from the mechanism. (Because it is implemented by it).
2. You can't infer the mechanism from the output. (Because different mechanisms can easily produce the same output).
My point here is 1, in response to the parent commenter's "the mechanism of operation dictates the output, which isn't necessarily true". The mechanism of operation (whether of LLMs or sunflowers) absolutely dictates their output, and we can make valid inferences about that output based on how we understand that mechanism operates.