Yes it is to do with cross contamination and infection control, in areas where there are vast amounts of people, vast amounts of pathogens of all different types, vast amounts of people doing the cleaning, and very often little facilities to hygienically cleaning the cleaning equipment.
In the case of the OP, if a sponge has been used on the floor of her mum's kitchen, whilst it's far from ideal to have been used for anything else, it will have been washed out before being used on dishes.
What is much more concerning is that sponges are being used this way in a more general sense, because it sounds like the sponges are not being plunged into boiling water after use to thoroughly clean them, and given that the problem appears to have been going on for a while, I have to question how long these sponges have been in use.
Even if sponges had been kept seperate, the process in this home is flawed anyway.The mother is more likely to fall ill from continually washing up with a sponge that is used day in, day out, and never sanitised.
And don't bank on professional cleaners to be any more diligent than the cleaner in the scenario here - I worked in the industry for far too long to know that it's no guarantee.