Such a person can get the parents'/grandparents' visa along with their partner who is the biological grandparent, i.e. if they're applying as a couple, with the biological grandparent sponsored by their NZ-resident child. Otherwise, I don't think so. See V3.110 d,
http://www.immigration.govt.nz/opsmanual/34627.htm, and V3110.1 b ii on the same page.
Bear in mind that the parents'/grandparents' visa doesn't actually lead to anything. It's just one way of allowing the older generation to spend half their time visiting NZ, which they legally can anyway on visitors' visas.
I understand you're going to be anxious till you get the word from the legal team, but try not to be too pessimistic. This sounds like the outcome of a 3 o'clock-in-the-morning worry, which you may never need to follow up at all. From what you've said before about your partner's situation, you've got a very good case there. No need to jump till you absolutely have to.