[dcl.pre] What's the meaning of (re)introducing names into the program?

In a simple-declaration, the optional init-declarator-list can be omitted only when declaring a class ([class.pre]) or enumeration ([dcl.enum]), that is, when the decl-specifier-seq contains either a class-specifier, an elaborated-type-specifier with a class-key ([class.name]), or an enum-specifier. In these cases and whenever a class-specifier or enum-specifier is present in the decl-specifier-seq, the identifiers in these specifiers are also declared (as class-names, enum-names, or enumerators, depending on the syntax). In such cases, the decl-specifier-seq shall (re)introduce one or more names into the program.

Please see this example

  struct {
      int c;
  };

Isn't that the member-declarator in the anonymous class does introduce the name c?

Every name is introduced by a declaration, which is a

• member-declarator ([class.mem]),

But the example is rejected by major implementations other than MSVC, I suppose the result is impacted by the above rule. The meaning of (re)introducing names into the program is arguably unclear. What can be sure is that the decl-specifier-seq struct { int c;} does introduce a name c, but whether introduce the name into program is not sure.
Maybe we should state when the names are considered to be (re)introduced into the program. After all, there is no normative rule related to this concept.

Maybe it could be reworded to be that

In such cases, the decl-specifier-seq shall (re)introduce one or more names that shall be bound to the scope where the declaration inhabits.

Start with the quoted [dcl.pre] wording and the anonymous-class example, then read the referenced [class.pre], [dcl.enum], and [class.mem] rules. The issue is resolved when the standard clearly defines what it means for names to be (re)introduced into the program and unambiguously determines whether the example is valid.