Why does the compiler select the base class constructor inside the template argument list?

Follow-up question to this one.

Basically, in the following code, why does the compiler think that the B inside A<B> in Cs constructor refer to the (inaccessible) constructor of the B base class?

struct B{};

template <typename T>
struct A : private T{};

struct C : public A<B>{                                                                             
    C(A<B>);   // ERROR HERE
};

Live example on Ideone. Output:

prog.cpp:1:9: error: 'struct B B::B' is inaccessible
prog.cpp:7:7: error: within this context

Note that the same error pops up if you change the constructor argument to A<B*>, A<B&> or even A<const B>. Also note that three of MSVC10, GCC 4.7 and Clang 3.1 ToT will error out, so it must be something in the C++ spec. What is it?