There's not much the banks can do about interest rates, it's got nothing to do with not wanting to see you at a mortgagee sale auction.
Because our banks are so small, they don't have a lot of capital. So they borrow money from overseas and sell it to you (for a handsome profit).
So whatever they buy the lending at, you pay at the other end.
Most of our banks have big parent owners in OZ though. But I do worry if there is a big financial crisis, whether they will be cut free. Especially as we are one of the only countries not to have any deposit guarantee scheme. The banks in Oz do have a guarantee scheme, so it doesn't make sense that we don't in NZ.