XML Parsing Error: no element found Location: ...

I am just working on an application which is supposed to be exposed to public users. I created a simple ajax process there which gets a value of an application element and does something based on the value. While calling the on demand process I am getting this error while not authenticated:

XML Parsing Error: no element found Location: moz-nullprincipal:{6492ed13-2b81-4989-938c-7c19121f419a} Line Number 1, Column 1:

After searching for this error in combination with APEX I found my old thread from 2012 which basically wasn't answered:

https://community.oracle.com/thread/2444115?start=0&tstart=0

After investigating what is happening there I noticed that the on demand process I created is set to "must not be public user" in the authorization section. Obviously APEX does that by default for the on demand processes. Running the ajax call would not find the "element" which is the actual process.