If you change ownership, group, permissions, etc. only on the contents, it does not help---since the new attributes are not applied to the containing folder.
Normally you would use the -R option like so:
chgrp -R <newgroup> /bin
This changes the folder AND everything inside.
Look at the permissions, owner, etc. for /bin and for the contents.
Here is how mine are set: (Note that everyone has execute privileges)
mherring@1[bin]$ ls -l|grep su
-rwsr-xr-x 1 root root 29568 2006-07-11 05:51 su
mherring@1[bin]$ ls -l|grep ping
-rwsr-xr-x 1 root root 21412 2005-11-15 14:44 ping
mherring@1[bin]$ cd ..
mherring@1[/]$ ls -l|grep bin
drwxr-xr-x 2 root root 4096 2007-02-21 09:52 bin
drwxr-xr-x 2 root root 4096 2007-02-21 09:52 sbin