This appears merely to test whether being told to take another's perspective, after already reading the other’s words, and having no opportunity to engage with

This appears merely to test whether being told to take another's perspective, after already reading the other’s words, and having no opportunity to engage with the other or gain new information, helps with "accuracy". Would it be surprising if it didn't help much? The whole point of taking another's perspective is to "get" it and it often involves asking questions.