One of the reasons we got cats was because our buliding was mouse infested. Sam caught three during the first week he lived here. We have not seen one since then. And there were definitely more than three in the house - I have picked up more than that from traps.
So, myth or not, we used to have a huge huge mouse problem, and we don't any more.
It probably depends on where the mice are coming from - if you are in a rural area with lots of field mice, I bet its different than in an urban area.