I think the key point here is that $1, $2, $3 etc are global variables. Referring to a global from within an anonymous sub doesn't make it a closure.

The following code generates a closure since $x is a lexical in the scope enclosing the anonymous sub:

  sub make_closure {
    my $x = 1;
    my $closure = sub { 
      return $x++; 
    };
    return $closure;
  }

  my $cls = make_closure();
  print &$cls;
  print &$cls;
  print &$cls;
[download]