[class.pre] p2 says:

For purposes of access checking, the injected-class-name is treated as if it were a public member name.

[class.member.lookup] p3 says:

[...] type declarations (including injected-class-names) are replaced by the types they designate.

Here, it is incorrectly assumed that an injected-class-name is a member, which it is not. Specifying that an injected-class-name is a nested type would resolve this.

A better definition would be something along the lines of:

A nested type denoting the class-name is declared as a public member; this is known as the injected-class-name.