"I also find the idea of a government agency prying into the sex life of 16 year olds more than a little creepy."
You will no doubt also find the idea of the education and health departments doing the same "creepy"? 12 and 13 year-olds given the immunisation against cervical cancer are asked if there was any chance they could be pregnant. School counsellors get intimately involved in situations surrounding the sex lives of adolescents. CYF, another "government agency" would also be closely involved with the sex lives of young people, and unfortunately, even children.
More generally, because I have seen other objections about case managers being involved in the 'new' policy,WINZ staff already deal with special grants for:
They also have to deal with difficult areas such as rape and incest when enquiring after the father of a dependent child, the naming of whom is a requirement for receipt of the DPB. They use their discretion over whether or not to impose a penalty for not complying if the aforementioned scenarios are involved.
I imagine then they are quite capable of exercising discretion over offering a referral to a family planning clinic or GP for the purposes of receiving free long-acting contraception.