That is, to pass for a human, the AI should imitate humans. This includes imitating their mistakes. AI's genuine mistakes would likely be different enough to help humans tell an AI from a human.
That is, the best strategy for an AI to pass the test is to be perfect, and perfectly imitate a perfect amount of human mistakes.
This definitely requires an ability to lie, to knowingly tell untrue things.
This ability is also required by much simpler circumstances: when directly asked, an AI should be able to lie and say "No, I'm a human", else it will fail the test instantly.
This likely means that a robot following the Asimov's three laws would never pass a direct Turing test.