Keep in mind that programs such as ''ls'' or ''stat'' display the permissions exactly the same regardless if the user that ran them is the owner or not, belongs to the group whose the file is or not. One has to tell apart manually which chunk of permissions to look at. 
roo@host /tmp $ whoami
roo
roo@host /tmp $ groups
bipedal jumping
roo@host /tmp $ ls -l
total 4
drwxr-x--x 5 roo jumping 160 Mar 16 20:04 myDir
-rw----r-- 1 roo jumping 249 Mar 16 20:03 someFile
roo@host /tmp $ stat myDir
  File: myDir
  Size: 160     Blocks: 0         IO Block: 4096   directory
Device: 0,30    Inode: 90         Links: 5
Access: (0751/drwxr-x--x)  Uid: (1234/  roo)  Gid: (123/ jumping)
roo@host /tmp $ stat someFile
  File: someFile
  Size: 249     Blocks: 8         IO Block: 4096   regular file
Device: 0,30    Inode: 91         Links: 1
Access: (0604/-rw----r--)  Uid: (1234/  roo)  Gid: (123/ jumping)
The user ''roo'' is the owner of the file, so for the user **only** the first chunk matters. 
tigger@host /tmp $ whoami
tigger
tigger@host /tmp $ groups
jumping happy
tigger@host /tmp $ ls -l
total 4
drwxr-x--x 5 roo jumping 160 Mar 16 20:04 myDir
-rw----r-- 1 roo jumping 249 Mar 16 20:03 someFile
tigger@host /tmp $ stat myDir
  File: myDir
  Size: 160     Blocks: 0         IO Block: 4096   directory
Device: 0,30    Inode: 90         Links: 5
Access: (0751/drwxr-x--x)  Uid: (1234/  roo)  Gid: (123/ jumping)
tigger@host /tmp $ stat someFile
  File: someFile
  Size: 249     Blocks: 8         IO Block: 4096   regular file
Device: 0,30    Inode: 91         Links: 1
Access: (0604/-rw----r--)  Uid: (1234/  roo)  Gid: (123/ jumping)
The user ''tigger'' is **not** the owner of the file, but is in group ''jumping'' whose the file is, so for the user **only** the middle chunk matters. 
eeyore@host /tmp $ whoami
eeyore
eeyore@host /tmp $ groups
quadruped glum
eeyore@host /tmp $ ls -l
total 4
drwxr-x--x 5 roo jumping 160 Mar 16 20:04 myDir
-rw----r-- 1 roo jumping 249 Mar 16 20:03 someFile
eeyore@host /tmp $ stat myDir
  File: myDir
  Size: 160     Blocks: 0         IO Block: 4096   directory
Device: 0,30    Inode: 90         Links: 5
Access: (0751/drwxr-x--x)  Uid: (1234/  roo)  Gid: (123/ jumping)
eeyore@host /tmp $ stat someFile
  File: someFile
  Size: 249     Blocks: 8         IO Block: 4096   regular file
Device: 0,30    Inode: 91         Links: 1
Access: (0604/-rw----r--)  Uid: (1234/  roo)  Gid: (123/ jumping)
The user ''eeyore'' is **not** the owner of the file, **neither** he is in group ''jumping'' whose the file is, so for the user **only** the last chunk matters.