Interesting post Alex, tongue in cheek, you might contemplate a trip to downtown Cibinong or Bogor where the process for getting a KTP and KK are relatively simple on a KITAP sponsorship.
You do not say but I am taking a guess that you are not married to an Indonesian lady and so hence not living with an Indonesian wife AND the Law may be interpreted differently on that basis whether you are legally entitled to a KK. In other words, if you do not live with an Indonesian person, you cannot have a KK. Is that what the Catsip lady is telling you? I do not think you can be denied your KTP. As we have covered on other topics, it is inconceivable that the Law is different in a different province of Indonesia, it is merely a matter of interpretation is most cases.
Following Atlantis guidelines, my wife holds a KK listing my child and I have a separate KK for the same address supported by my KTP. The 'catch' may certainly be if living at an address with people with whom you are not married and who are not Indonesian but it seems far from logical.
Not sure why as a foreigner you would want or need a KK if no Indonesian (or other person) living with you and you are issued with a KTP WNA?