PHP has two ways of tracking user's session to allow you to access their session variables. One method is to use cookies, the other is to use a transparent session id.
Cookies aren't guaranteed to always be there since some companies have a corporate policy, misguided as it may be, that cookies are some kind of big security issue.
Transparent ids, which is the method you describe, works by always post-pending the session id to the end of every URL back to the server.
The choice is decided at compile time, and I'm not sure there is a php.ini directive to change it's behaviour after building PHP.
To turn on transparent session id propagation, you would use the --enable-trans-sid switch at with the configure script.
So, all you need to do is rebuild php without that switch.