Facebook login question

Hi

I have a Flash iOS AIR app that needs to display membership data (from my database) to users when they log into it.

I have a standard username/pass login, but now want to add Facebook login, the same way I have on the web app version of my app.

I bought a class for logging in using Facebook. It returns the user's Facebook details to the app fine, but I now want to take the user's Facebook ID and use it to create/log them into their membership account on my app.

It occurred to me that it's not really safe trusting that the Facebook ID the client sends from their phone is their own.

Is anyone experienced using Facebook credentials to log a user into your app in this way? It seems most apps using Facebook login don't actually log a user into a database with the credentials - they just post to Facebook etc.

The support for the class I bought isn't really giving answers I can work with.

Thanks for your time and help.