In many classification tasks designed for AI or human to solve, gold labels are typically included within the label space by default, often posed as "which of the following is correct?" This standard setup has traditionally highlighted the strong performance of advanced AI, particularly top-performing Large Language Models (LLMs), in routine classification tasks. However, when the gold label is intentionally excluded from the label space, it becomes evident that LLMs still attempt to select from the available label candidates, even when none are correct. This raises a pivotal question: Do LLMs truly demonstrate their intelligence in understanding the essence of classification tasks? In this study, we evaluate both closed-source and open-source LLMs across representative classification tasks, arguing that the perceived performance of LLMs is overstated due to their inability to exhibit the expected comprehension of the task. This paper makes a threefold contribution: i) To our knowledge, this is the first work to identify the limitations of LLMs in classification tasks when gold labels are absent. We define this task as Classify-w/o-Gold and propose it as a new testbed for LLMs. ii) We introduce a benchmark, Know-No, comprising two existing classification tasks and one new task, to evaluate Classify-w/o-Gold. iii) This work defines and advocates for a new evaluation metric, OmniAccuracy, which assesses LLMs' performance in classification tasks both when gold labels are present and absent.