I've found another reason for user's crontab not running: the hostname is not present on the hosts file:
user@ubuntu:~$ cat /etc/hostname
ubuntu
Now the hosts file:
user@ubuntu:~$ cat /etc/hosts
127.0.0.1 localhost
# The following lines are desirable for IPv6 capable hosts
::1 ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters
ff02::3 ip6-allhosts
This is on a Ubuntu 14.04.3 LTS, the way to fix it is adding the hostname to the hosts file so it resembles something like this:
user@ubuntu:~$ cat /etc/hosts
127.0.0.1 ubuntu localhost
# The following lines are desirable for IPv6 capable hosts
::1 ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters
ff02::3 ip6-allhosts