How to modify app permissions on a rooted device without third party? Is there any way to modify app permissions on a rooted (running Android 4.3) device "by hand"?

Or maybe I should ask how third party apps (like "access denied" or "Gemini") can block app permissions?
You can use adb (Android Debug Bridge) tools. 

-Install platform-tools which are included in Android SDK
-Toggle USB Debugging options on your phone.
-Connect to your phone with adb.  

Example operation for testfile.txt 

Upload your file with 'adb push ' command.

adb push testfile.txt /data/local/tmp/


Get shell with 'adb shell' command.

adb shell


(You will get a prompt like below.)

Become superuser with 'su' command.

shell$ su


Change permissions of testfile.txt to 644 (-rwx--r--r-)

chmod 644 /data/local/tmp/testfile.txt