I do not know about ladies' public toilets, but the floors in mens' public toilets are always disgusting. They smell, they are wet, there is likely to be all manner of dirt on them. Not just the obvious, but cleaning chemicals and mud. You definitely would not want to touch the floor of a public toilet with your hand.
Now imagine somebody goes to a public toilet. He then visits your house or apartment and comes in with his shoes on, walking on the same floor on which your children play. See what I am getting at?