Again, do you understand what network support entails? Not just techie level, or even admin level. Proper network management(not sure on exact title

)?
While CSs might have designed these protocols, your implying that every CS knows how they were put together. Surely your not claiming that?
Bottom line is both wont work without the other. And neither require more expertise or intelligence. I doubt you'd find many CS's who know how to administer a network, even at a basic level, again, because thats not what they have been trained to do. And again, visa-versa. Probably no techies who know where to start with a CS subject.
CS's are not more intelligent, and CS isnt more complex than high level network management.
Intelligence, complexity and whatnot are all relative.