As for me, mopping the kitchen floor is all about risk assessment. On the one hand, a quick dry with a teatowel reduces the risk of nastly falls on our tiles. On the other, we risk a stomach bug by using a tea towel as a mopper up.
Finding a window in my week to clean the floor is bad enough. Finding one that is minus both children and husband is almost impossible. Do they heed warnings to avoid a wet floor? No. The number of nasty near misses we have had - toddler's forehead meeting corner of kitchen table etc etc.
With my family I think the risk of injury is greater than the risk of a stomach bug. Trust me!!I never leave a kitchen floor to dry. I mop it barefooted and them slowly skate around the wet floor with a tea towel under each foot, until a state of dryness is approached.
The teatowels do go straight into the washing machine after, though.
As for your orignial question Robin, yes it was a very thoughtless practice, especially with a ready supply of paper towels so easily to hand. Did the guilty PTA-er know the kitchen well? If she did, there isn't much excuse to use the tea towel in the first place. Despite using them at home, I believe I'd never use a tea towel to mop a floor in public. Perhaps she saw the danger of people slipping on the kitchen floor as the greatest risk. She might have been thinking of you?
I don't think I would have been as brave as to tell her it was disgusting. For me, a bit like a pot calling the kettle black.