As best I can make out, the requirement for ASX listed companies...

As best I can make out, the requirement for ASX listed companies is for there to be two Board Members resident in Australia. Note, they don't have to actually be Australian Citizens, it seems, just residents.
Mr Peters is resident in Australia. Ms Mehrtens is most probably resident in Australia. Therefore, if she were already on the Board then the requirement would already be fulfilled and there would not be this current problem.
I know on NRZ's website there is a page listing the Board Members and she is on that page. But I think that might be a bit of artistic licence.
The Company Secretary's role is a lot more involved than many people think and Secretaries work very closely with the Board to ensure correct governance and compliance. There is actually a small ASIC fine for getting this wrong, but it isn't much of a deterrent. It's in the order of a few hundred dollars.