Putting aside guilt or innocence you are wrong about how people used answering machines at the time and you are refusing to admit it. And yes they could easily switch it on when they went to the shop for ten minutes, it's inly a button to press.
Did they switch it on when going to bed, in the shower, hoovering or listening to music ? As it is unlikely they will hear the phone in these situations.
These together with switching it off/on when going out is a hell of a lot of switching off/on.
Thank goodness 901 and 1571 was introduced.