No, I don't think a baby must start solids at 6 months. Most babies will thrive on breastmilk for many more months. I don't think there's any reason to start water at 6 months either, UNLESS a baby has also started a significant amount of solids ("significant" meaning more than the little occasional mouthful). I started offering water when the poops changed, which was usually around when my kiddos started actually swallowing more than a mouthful each day. (What they put in their hair and all over the floor doesn't count!

). I have found that once any solids have been introduced a child can get constipated without additional water. I always offering sips from my cup, although I did offer a sippy cup starting around 9 months, just for baby to mess with and try to figure out.
I don't think a sippy cup is a nipple preference/nipple confusion issue, unless you have a child who's overcome serious sucking issues and you are worried about undermining that. I wouldn't worry for a second with a baby who had a "normal" start with breastfeeding.
If you really want to be careful about that, offer only water in the sippy, not milk.
But I think it's really not something to worry about. My DS and I fought nipple confusion and bottle preference in his early weeks, and he went on to nurse into toddlerhood, and he had no problem with a sippy being introduced in the second half of the first year.