I haven't actually seen that. It seems the cups are usually stacked upside down so they pick it up from the bottom and put it on the tray and then fill it with water. Or sometimes they point the stack at me and I pick up the cup and they fill it.
Ultimately, my assumption is there is some touching at some point in tight quarters and bouncy air space. I'm not in love with the concept but it's better than no water or the old days when I was kid of filling water from a spigot in the middle of the cabin outside of the lavatories.