[EDIT]:
Me and a colleague found a workaround, at least for our case. We checked the logcat logs and we noticed an error with "AsyncTask". From what I could check, the Facebook Android SDK is trying to call publishInstall in another thread, and if this is the first call you make in your app using AsyncTask the crash occurs.
According to this post: http://grokbase.com/p/gg/android-developers/11ajf99wrs/possible-bug-in-asynctask the workaround might be to execute a dummy task through AsyncTask to "fool the system". This worked for us and the application is not crashing anymore. Hope it helps.
[/EDIT]
In case you're still searching for an answer:
Does FB.PublishInstall Require AuthToken?
benp stated that publishInstall does not require an access token, so I'm guessing based on what he said that PublishInstall can be called before authorization.
I'm having the same issue, but the crash occurs only on certain devices. Some devices just print the error message without a crash. This may be a Facebook SDK bug.