We've found one more cause for "No input file specified." on CloudLinux systems (with CageFS installed). A fix for that is adding /var/www/html into /etc/cagefs/cagefs.mp and doing the following afterwards:
/var/www/html will be added into /etc/cagefs/cagefs.mp by default with the future versions of CageFS.
Code:
cagefsctl --remount-all
/var/www/html will be added into /etc/cagefs/cagefs.mp by default with the future versions of CageFS.