Comment # 4 on bug 1206688 from Michal Suchanek

It is normal for chmod to ignore bits it cannot set:

>       If  the  calling process is not privileged (Linux: does not have the CAP_FSETID capability), and the group of the file does not match the effective group ID of the process or one of its supplementary group IDs, the S_ISGID bit will be turned
>       off, but this will not cause an error to be returned.

>       As a security measure, depending on the filesystem, the set-user-ID and set-group-ID execution bits may be turned off if a file is written.  (On Linux, this occurs if the writing process does not have the  CAP_FSETID  capability.)   On  some
>       filesystems, only the superuser can set the sticky bit, which may have a special meaning.  For the sticky bit, and for set-user-ID and set-group-ID bits on directories, see inode(7).

However, the vfat situation is not explicitly documented.