In the current draft, the definition of a member-qualified name is that

A member-qualified name is the (unique) component name ([expr.prim.id.unqual]), if any, of

• an unqualified-id or
• a nested-name-specifier of the form type-name ​::​ or namespace-name ​::​

in the id-expression of a class member access expression ([expr.ref]).

Here, "in" can be interpreted by its English meaning, which can result in an issue arisen from this example

struct C{
    int member;
};
struct D:C{};
struct E:D{};
struct F:E{};
int main(){
   E e;
   e.F::D::C::member = 0;  // #1
}

the id-expression of the class member access expression at #1 is F::D::C::member obeying the grammar nested-name-specifier template _opt unqualified-id , that is, member is the unqualified-id in this id-expression of the class member access expression. Does it mean member is a member-qualified name? It seems this is not the intent of that rule. Conversely, F can be a member-qualified name since the nested-name-specifier to which it belongs obeys the form type-name ​::​ and is in the id-expression.

My opinion is that the above rule may be improved to be that

A member-qualified name is the (unique) component name ([expr.prim.id.unqual]), if any, of

• an unqualified-id that is the id-expression or
• a nested-name-specifier of the form type-name ​::​ or namespace-name ​::​ in the id-expression

of a class member access expression ([expr.ref]).