Under which user does it run? It is usually different from the one the webserver is running.
chmod operations are only allowed by the file owner, no matter what rights were given. So you can get this error if the file owner is for example httpd, www-data, ....
I got diffrent error message from file.php like followings.
[2021-03-25 04:00:01] fuelphp.ERROR: 0 - Invalid path: "/sys/kernel/security/apparmor/apparmorfs:[11563]/namespaces/", directory cannot be read. in /usr/local/batch/fuel/core/classes/file.php on line 270 [] [] [1;31mUncaught exception Fuel\Core\InvalidPathException: 0 - Invalid path: "/sys/kernel/security/apparmor/apparmorfs:[11563]/namespaces/", directory cannot be read. in /usr/local/batch/fuel/core/classes/file.php on line 270[0m
If you have /usr/local/batch/service/fuel/core... and /usr/local/batch/service/public/index.php, then that code is ok. If you moved stuff around, you need to adjust the paths accordingly.
The fact that you get the wrong path suggests public and fuel are not where are are by default.
That is a different question than you initially asked.
On modern distro's, you can't just write in any location without the correct security policies in place (apparmor, selinux). So you need to write a security policy for that.