I don't know about the details of this device, but in general, simply being high-voltage doesn't automatically mean it's dangerous. One of the machines I work with in my day job has probes that put out around a thousand volts, but it's totally safe to touch them with your bare hands. You won't even feel a tingle.
That said, it's always prudent to treat any live electrical line as dangerous unless you know for a fact that it isn't, of course.
Why is the 1000v safe? My guess is energy released is small e.g. a small capacitor. Or internal resistance is high so it becomes much less when you touch it. Or you mean touch one end and it is DC.
I'm no EE, but my understanding is that it's partially because the amperage is very low and partially because the signal is AC operating at a frequency that causes a large impedance mismatch between the probe and people.
It's counterintuitive enough that the probes actually have an "anti-warning" label to inform people that they are safe to touch.