The spec says at 9.2p1

"The member-specification in a class definition declares the full set
of members of the class; no member can be added elsewhere."

However in the same paragraph it contradicts this

"Members of a class are data members, member functions ([class.mfct]),
nested types, enumerators, and member templates ([temp.mem]) and
specializations thereof."

Specializations are added elsewhere as in the following example

class A { template<typename T> class X; };

template<> class A::X<int> {};

Here, a specialization of A::X is declared ouztside of the
member-specification and according to the same paragraph, the
specialization is a member. Another example with partial
specializations

class A { template<typename T> class X; };

template<typename T> class A::X<T*> { };

Here, a partial specialization is declared outside of the class, which
for partial specializations is valud. Because it's a member template,
and member templates according to that paragraph are members, here a
member is introduced outside of the member-specification aswell and
contradicts the paragraph directly.

Another rule at 9.2 that seems to be in error is 9.2p2 which says "...For any other member-declaration, each declared entity that is not an unnamed bit-field ([class.bit]) is a member of the class, and each such member-declaration shall either declare at least one member name of the class or declare at least one unnamed bit-field."

This indeed does not apply to partial specializations either. They do not introduce a member name. Albeit template-ids are names, they do not seem to be "introduced" by declarations the way other names are, since they are not found by name lookup.