I just question if he is as thirsty as they think. I've offered a sippy cup while outside in the past and he'll take a small sip push it away and want to play. I can't help but feel like they get home and give him a bottle of formula and he is sucking it back since he enjoys the cuddle with mom and hasn't had formula all day.
I have take and toss cups I can bring out to offer. I will offer the water shortly before he is picked up to see if they notice a difference.