I had this issue and my problem was that I was calling my method with any() instead of anyInt(). So I had:
doAnswer(...).with(myMockObject).thisFuncTakesAnInt(any())
and I had to change it to:
doAnswer(...).with(myMockObject).thisFuncTakesAnInt(anyInt())
I have no idea why that produced a NullPointerException. Maybe this will help the next poor soul.