I've heard some similar things (about not good for digestion)which make sense, but I don't know what's definitely true or not.
The for-sure thing would be not to drink something ice cold with your meals (room temp or maybe slightly warm would be best I'm guessing). I personally don't like drinking with meals; doesn't feel right. I try to be well hydrated before I eat, then not drink my water until 15-30 mins after...
I always have a 16oz glass of cold water next to me when I eat but usually find that I only drink it when I need to help wash something down. Then when I am done eating I usually finish the glass of water. Doesn't seem to affect my digestion and actually I think it helps keep me feeling full.