C++ private modifier ignored on nested anonymous struct

The following sample code compiles just fine in Visual C++:

class Test {
private:
    struct {
        struct {
            int privateData;
        };
    };
};

int main(int, char **)
{
    Test test;
    test.privateData = 0;
    return 0;
}

But why? I'd expect a compiler error because the privateData member should be inaccessible to the function main, since it's supposed to be private like its container's container. I know that nameless structs are not part of official C++, but this design is asinine.

By the way I've also tried to change private into protected and struct into union: it looks like the compiler refuses to honor access modifiers on anonymous structs and unions that are nested inside another anonymous struct or union.

Can someone explain this feature?