Yes, that's correct. The Colt family were in touch with various agencies, schools, and Centrelink, just not consistently. It just goes to show that this little girl could also have been registered--birth certificate, medicare details, periodic day care enrolment, doctor visits etc, but never been in contact with any person outside the family for long enough for the problems at home to be fully identified or remembered.
It's also worth noting that the Colt children were not actually removed from their mothers due to incest--DOCS had no idea about that at the time. The children were actually removed due to severe and chronic neglect. It was only
after the children were placed in foster care that they started to disclose to their carers, DOCS staff, and counselors about chronic sexual abuse in addition to the other issues. Anything can go on in any family and no one outside that family ever know. Several generations of children in this family suffered abuse but no one knew about it until 2012.
Seeing as there has been so much speculation about this child being the victim of abuse, I've added the link for the NSW case findings for the Colt family. Confidentiality around children in foster care is very strict in Australia, but they took the rare step of publishing the Children's Court filings for the Colt case. (Also "Colt" and all the other names used in the media are pseudonyms; the real family name and the children's name are never to be made public in order to protect the children.)
http://www.caselaw.nsw.gov.au/decision/54a63b193004de94513db1b2