You probably mean:

"A quantum measurement influences the system being observed: The act of observation injects a kind of random noise into the system. This is ultimately the source of Heisenberg’s famous uncertainty principle."

I'd agree that's an inaccurate description of the uncertainty principle, but then the following sentences are:

"The uncertainty in a measurement is not, as Heisenberg initially thought, an effect of clumsy intervention in a delicate quantum system—a photon striking a particle and pushing it off course, say. Rather, it’s an unavoidable outcome of the intrinsically randomizing effect of observation itself."

I'm not sure I could explain it better at this level...