FAQ: In C, stuff is either stored in structs (safety problem - no encapsulation), or it is declared static at the file implementing an interface (usability problem - there is no way to have many instances of that data).
With C++ classes, you can have many instances of the data (many objects) and encapsulation (non-public members).
FQA: This is wildly wrong, and the chances that the FAQ author didn't know it are extremely low. That's because you can't use FILE* from <stdio.h> or HWND from <windows.h> or in fact any widely used and/or decent C library without noticing that the FAQ's claim is wrong.
When you need multiple instances and encapsulation in C, you use a forward declaration of a struct in the header file, and define it in the implementation file. That's actually better encapsulation than C++ classes - there's still no run-time encapsulation (memory can be accidentally/maliciously overwritten), but at least there's compile-time encapsulation (you don't have to recompile the code using the interface when you change the implementation).
The fact that a crude C technique for approximating classes is better than the support for classes built into the C++ language is really shameful. Apparently so shameful that the FAQ had to distort the facts in an attempt to save face (or else the readers would wonder whether there's any point to C++ classes at all). The FQA hereby declares that it will not go down this path. Therefore, we have to mention this: the forward declaration basically makes it impossible for the calling code to reserve space for the object at compile time. This means that a struct declared in a header file or a C++ class can sometimes be allocated more efficiently than a forward-declared struct. However, this is really about a different tradeoff - safety vs. efficiency, and there's no escape from this tradeoff. Either the caller knows about the details such as the size of an object at compile time - which breaks compile-time encapsulation - or it doesn't, so it can't handle the allocation.
Anyway, here's the real answer to the original question: C++ helps with the tradeoff of safety vs. usability by eliminating both.
C++ is extremely unsafe because every pointer can be used to modify every piece of memory from any point in code. C++ is extremely unusable due to cryptic syntax, incomprehensible semantics and endless rebuild cycles. Where's your tradeoff now, silly C programmers?