If a script would be saved as an application with the Script Editor, its owner is (me) r/w, its group is wheel r/o and everyone r/o.
If I look into any other application (installed by me) into the Applications folder for example, its owner is (me) r/w, its group is admin r/o and everyone r/o.
If I change the group of the script application from wheel to admin, it won’t launch.