Comment on "Is a system's wave function in one-to-one correspondence with its elements of reality?" [arXiv:1111.6597]

Recently, it has been argued [arXiv:1111.6597, arXiv:1005.5173] that different quantum states do necessarily correspond to different elements of reality, under the assumption that quantum mechanics is correct and that measurement settings can be freely chosen. Here, we prove that additional assumptions are necessary to derive this results, which then has not general validity.