Rules Inconsistency

Found an inconsistency in the rules a while ago. Now that I have an account here, I can finally share it :]
If you look in the acting cap section here, you can see the following statement, “If there is no Head of Security, the acting captain may order executions.”

Right here, in the executions tab, you’ll find the following, “5. Authorization must be given by the Captain. If a Captain is not assigned, dead, missing, or otherwise rendered incapable of providing authorization, the Acting Captain may authorize an execution in their stead.

Those are conflicting statements. So, in case the captain heroically leaps into the SM, and the mime lets out a barely audible whimper while being tortured by the clown, does the HoS or acting cap authorize the execution?