If you delete the log while the app has it open, the app will continue to write to the deleted file (basic Unix here), but the file will stay hidden.
If the app then cycles the log (when/if the process gets killed), this will open a new log file, reclaiming the FS storage for the deleted file.
The post-mortem crash log is always written, regardless of the setting for the detailed event log -- it's just too valuable to lose, and is often needed without an advance warning.
The summary for the checkbox corresponds to the checkbox's "checked" state, so this is normal. I'll adjust the wording so it's more clear.