Unless I’m mistaken the “deep access” is just bad reporting (the media are surfing on the wave of Facebook bashing).
What they mean by deep access is that the Facebook sharing system extension built into some OSes (including iOS pre iOS 9) had the possibility of accessing a lot of information from the connected Facebook account, which is not really anything to worry about (if your device’s OS is malicious you have way more to worry about).
That's funny, because very recently, there was a discovery that fb gave most of the device makers deep access to user data, including Apple.
Against all evidences, Apple still gets a pass.