Determine if Flash is in private browsing mode

We're currently showing our users some instructions on how to allow our website access to the camera through the Privacy panel, but we noticed that in private browsing mode, the experience is different (a one time allow/deny panel comes up).

In order to provide better instructions to our users on how to deal with the Flash security panels for both cases, we would like to detect which panel will be shown so we can shown the appropriate instructions.

I've read the article here introducing the new feature, but it says nothing about if we can programmatically detect private browsing mode is enabled.

Private browsing in Flash Player 10.1 | Adobe Developer Connection

I'm wondering if there is an alternate way to get to that data, perhaps through the Shared Objects API or some other "hacky" approach. Any help would be appreciated.

Thanks!