As someone who has had 8 different cats over the years, I can verify this is not necessarily true.
In my experience it usually meant the cat preferred running water over standing water in a bowl. Sometimes it meant the cat didn’t like the size or shape of their bowl.
Sometimes it means your cat is a defiant nut who doesn’t like things you put out for him, but will gladly drink out of the dog’s bowl, a glass of water, or the toilet.
I avoid eye contact and hope I didn’t disrupt his day