  Cryptographic security of quantum key distribution is currently based on a
trace distance criterion. The widespread misinterpretation of the criterion as
failure probability and also its actual scope have been discussed previously.
Recently its distinguishability advantage interpretation is re-emphasized as an
operational guarantee, and the failure probability misinterpretation is
maintained with a further failure probability per bit interpretation. In this
paper we explain the basic perpetuating error as a confusion on the
correspondence between mathematics and reality. We note that the assignment of
equal a priori probability of 1/2 to the real and ideal situations for
distinguishability advantage would not lead to operational guarantee. We
explain why operational guarantee in terms of Eve's probabilities of getting
various key bits is necessary for security, and why the failure probability
interpretation misrepresents the security situation. The scope and limits of
the trace distance guarantee are summarized. It is shown that there would have
been no security problem to begin with if the failure probability per bit
interpretation validity.
