BASIC PROBLEM: I want my app to be able to make calls to the Facebook graph api about authorized users even while the user is away.
For example, I want
I finally figured this out on my own. The answer is pretty anti-climactic. It appears that newly created apps get 60 day access tokens automatically. I'm not sure if this is dependent on enabling the "depricate offline_access" setting in the Migrations section of the app settings. Leave it on to be safe.
So at the time of writing this, you can use the PHP SDK as follows: $facebook->getAccessToken();
(The reason my app wasn't working as expected was unrelated to the expiration of the access token.)
Just one more thing, to get long-lived access token using PHP SDK you should call $facebook->setExtendedAccessToken(); before $facebook->getAccessToken();