You are using selinux. If you "setenforce 0" and then let cron run, you will get the output you expect. At the root shell, your selinux context is:
unconfined_u:unconfined_r:unconfined_t:s0-s0:c0.c1023
But when running from Cron, your selinux context starts as:
system_u:system_r:system_cronjob_t:s0-s0:c0.c1023
| to another command works, so you could have also done "| cat > file"
aide then does its own thing with selinux which causes redirection to fail.