If that is the case, then it just further invalidates the argument for Kik because it is most certainly not a famous mark.
Famous and "Unique" aren't the same thing. I was responding to the theory that because "Google" is a made-up word, they'll receive extra protections. That's false. That said my example was a bad one, since Google is a famous mark Google Paper Co. would likely be infringement.
Feel free to start Kik Paper Co, however.
I guarantee you won't last long if you start a Coca-Cola School of Hairdressing, even though the beverage company doesn't compete for that business.