To add to Bob Bee's Answer: to understand this situation, it helps to divorce light from special relativity and take an Ignatowskian approach to the latter, as I discuss further here. There is a universal signal speed limit $c$, and, experimentally light is found to move at that speed, or at least the two speeds are mighty near one another. That latter, experimental, result can be taken as asserting that light is mediated by something with zero rest mass.
So now, anything else to do with light - speeds in media and so forth - is simply not relevant to the causality issue, which arises wholly from the relativity from symmetry alone standpoint conceived by Ignatowski. The issue with $c$ is that relative speeds greater than $c$ can reverse the time-ordering of events for different observers, which is a real problem for a notion of causality if the two events in question are causally related: such as my switching on my gas ring and sometime later eating the boiled eggs that I have cooked. So, we simply postulate no faster than $c$ travel to keep our notions of causality in accordance with what we observe.