The reason you are getting mix responses from the web is because it's yes and no on how PHP works with sessions.
The way PHP works is it looks at the browser agent, from a an internal lookup it determines if that browser can support cookies, if it does it defaults to using using a cookie based session. It DOES NOT determine if it does support cookies and the user has enable cookies turned to off.
When it does detect that a cookie cannot be used then it puts the sessionid in the URL and uses it.
At one time I believe there was a way to force PHP to use either the cookie or url encoded string but not sure how it works now because I use cookies and force the players to use cookies if they want to play any of my games. If the option is available look in the PHP.ini file if you can, if you are on a hosted web site you probably won't have that option (ie to look / change the PHP.ini file).
There is also a PEAR library that'll use a database to store session data as well but I never used it that one either.
http://pear.php.netHope this helps ya out a bit...