Good news: I was just admitted to the Asiana C lounge at ICN the day before my flight. They wouldn't print my boarding pass, and they initially told me that I couldn't access the lounge today. But I had printed out the access rules from the site and had the *A employee handbook on my computer, and I showed them the "24-hour" clause. They accepted it after about 15-20 minutes of phone calls to who-knows-who, and phoned the lounge attendant to warn her of my arrival. This is the same lounge that denied me access in the same situation last week, but I am very happy with how everything worked out this time.

Doesn't answer any questions about why the wording is so bizarre, though.