Yeah, and I've got a feeling Bard (and maybe ChatGPT for that matter) might be using (2) since I didn't attempt to obfuscate the structure too much. Ironically the fact that it recognizes it as the false belief test is what makes me suspicious it's just matching against the semantic structure.
I guess there are two ways of passing this test: 1) use your reasoning skills to figure out the answer or 2) practice tests beforehand so you can recall the answer.