A few years ago Caltex used to make oils for Honda but then Honda contacted Total for their oils as they are cheap. And almost no body uses Total oils in open market, so it was good for Total as well to make a deal with Honda.
For the first two oil changes for my Honda City, I used Honda oil but then I switched to Caltex Havoline Fully Synthetic. Its API SN. A newer and better oil. I felt that at high RPM, the engine is more smooth with this oil. Fuel economy remains same.
If you buy this oil from authorized Caltex pumps or Metro Cash n Carry store, then it isn't fake.