The output "MUST" swing much more as opposed to "can".
Is this the implementation you will use? Now that you understand this circuit, look at the simpler two transistor solution using T1 and T5 in http://www.bogobit.de/bogobox/
I will most like not be using it. I just HAD to understand it. I am using a NPN transistor that sinks base current from a PNP. The NPN is driven by an op amp. Pretty much how T1 and T5 are configured.