It might be a bit complicated, and there might be other (better) ways, but you could try something like this. Using getURL you can execute javascript in the user's browser. However, as far as I know, this can not return anything to the swf directly. Thankfully, javascript can also interact with flash (the other way round), as described here : http://www.permadi.com/tutorial/flashjscommand/
Now, you'd need a way to find the swf's name in the browser for this to work, but I can imagine that by looping through all objects and seeing if they have a certain property (using GetVariable), you can find the right object. There may be an easier way too, don't know. After you find the swf, you can send it a variable with the document.location.
So to make it all work, your swf should contain a one-line string (with the javascript that finds the swf, gets the location, and sends it to the swf), and pass this string to the browser using getUrl("javascript:"+browserCheckScript); or something like that.

Your javascript-string can also just check the document.location, and if it's not the one you intended, you can change it to your site, which should also store the referer in your logs. This way, you won't have to bother finding the swf object with javascript.

Note : I have not tried any of this myself, and it's a bit clumsy, but it might work