I have heard this but it is a total myth. I have and know of many other folks that breed mice and rats in the same area(not tub). The reason some may believe this is because mice wont breed in as extreme temps as rats do so while rats my be breeding fine if it gets too cold or hot for the mice may stop breeding. This has nothing to do with the rats. Its just that mice are so much smaller that their bodies dont adjust as well to extreme temps like rats can.