In the APIs section is the following statement "Neither API provides real-time access to the raw data, and neither API can interact with the hardware without the Saleae Logic software running".
I'm guessing this statement exists because you've received numerous requests for it, and I'm one of them. Essentially I need to monitor 5 signals for a complex event (deep mathematics on analog signals combined with digital data) and then save the 5 minutes leading up to that event.
In the past I've been able to do this type of real-time capture and monitor on other types of devices (E.G. TotalPhase Beagle).