Note that the numbers you actually came up with -- +9V, and -9V, from an 18V supply -- are theoretically possible with perfect linear regulators. Imperfect regulators will end up causing voltage drops when you start pulling load, but I wouldn't be surprised if the circuit that you're measuring would stay at, say, +7V/-7V with some amount of load on it. That's still totally congruent with an input of 18V.
I could write an even simpler version of that 18V to +9V/-9V circuit right here. Check the attachment for the implementation. Get a couple of 1A 9V Zeners and you're in business!
The numbers in the diagram -- +15V and -15V, coming out of a single 24V supply -- are not going to work with linear regulators. You need non-linear converters, such as switching/PWM regulators, to create a greater total potential than you get from the single voltage source. If you look at what Grumpy Mike said, it's exactly that. So, it sounds like you're hearing something differently from what people are actually saying, and then deciding to take offense at perfectly valid engineering advise. In the end, he who loses out is you, because that's not a way to be successful in life, but if that's really up to you to determine.
