Next time give us output of your ls -l /bin/fusermount
.
Executable /bin/fusermount
permissions normally (fusermount version: 2.8.3, on Centos 6.6) are:
$ ls -l /bin/fusermount -rwsr-x--- 1 root fuse 32336 Dec 7 2011 /bin/fusermount
Which mean you must be root or in the fuse group to execute it.
If you gave the write permission to everyone on the executable /bin/fusermount
, that is 100% wrong, because it permits anyone to damage it or replace it with an exploit. Those with execute permission on it (i.e. users in the fuse group) might gain a root shell.
If by ... has been given to everyone you actually gave everyone write permission to the directories inside the mounted filesystem (in attempt to let them unmount), those directory permissions are irrelevant to control of the mount itself via fusermount.