Understanding of coupling coefficient and power transfer efficiency
The power into a 100% pure ideal transformer with a coupling factor of less than unity is exactly the power taken by the load. If the power out is 1 mW, then the power in will be 1 mW.

Or am I having any misunderstanding here?

Your math is wrong in that you have made assumptions about the phase relationship between V and I on the primary side and directly equated that to power in. That is not true. Imagine the situation when k is 0. All you have is an inductor with a voltage across it and some current flow determined by the inductor's reactance and operating frequency; there isn't any power because V and I are at 90° to each other.