Since you're only outside for an hour, just after they had access to water, I don't think you're wrong. Parents are being fussy. Keep track of their wet diapers for a few days, and see what you find. If you have a lot of wet ones, let them know what you found, and that their worries are unfounded.

We're outside most of the morning, mostly in the sun, so I bring water. Everyone has the same straw water bottle every single day, year round (they get it for snacks in winter), so for the most part, everyone knows which one is there's. They aren't allowed to play while carrying it. It's just available, and every so often I'll ask if anyone wants water, and hold it for whomever comes over.