Any clothes shop won't let you eat or drink in there either, but I wouldn't think twice about feeding my baby in one if he/she needed it.
As for breastmilk being a bodily fluid, if you're breastfeeding chances are you could leak into the pool anyway, so perhaps we should ban all lactating women from pools?
Even if you try and avoid it, babies are likely to get pool water in their mouths/on their hands then in their mouths regardless.
As for good reasons to 'feed' a baby in the pool, maybe to comfort them if they are anxious at first? Maybe because you have other children to supervise? Maybe because they are likely to only want to feed for a minute or so and it's easier to just feed them there than it is to get out and feed? Maybe because you want to stay warm in the pool instead of sitting on the side and getting cold? (in any case, feeding on the side of the pool apparently wouldn't have been acceptable to the staff in question here either
)