Options apply to all profiles. However, each profile has a setting to choose which tables and charts to create. So in your case you can do the following:
1. Create the table you wish in Options > Report > Tables. E.g. you can copy the existing 404 table and modify it.
2. Uncheck the table you created in Options > Report > Contents, so by default it won't be shown in profiles.
3. In a profile you need enable the table in Profile Properties > Report > Custom report contents.
It seems that you have modified the table in Options > Report > Tables by adding grouping by referrer. As the result requests without referrer aren't shown.
The grouping can be removed in the table properties, Data tab.
1. Create the table you wish in Options > Report > Tables. E.g. you can copy the existing 404 table and modify it.
2. Uncheck the table you created in Options > Report > Contents, so by default it won't be shown in profiles.
3. In a profile you need enable the table in Profile Properties > Report > Custom report contents.