As Sharky alluded to above, in respect of the entire drivetrain, these statements feel like they ought to be common sense, but they are not so much wrong as economical with the truth.
You can climb hills with whatever crank length you like, because you also select a gear ratio that matches your power output, and your cranks are, as a first approximation, designed for your leg length (and everyone else's leg length). This is why children's bikes come with short cranks and adult bikes come with long(er) cranks. Most adults are five or six feet tall which is why, with some allowance for greater or lesser bending of the legs because people can adapt, cranks have ended up at about 170mm.
You could fit a larger or smaller back wheel for climbing hills and it would have the same effect as changing gear. The difference between short and long cranks, once force at the pedal is accounted for through the drivetrain, is the rotational distance covered by your feet, and the amount of flexion incurred by your knees and hips. A smaller foot distance suits a higher cadence because short cranks reduce the linear travel of the mass of your legs, once your muscles are acclimatised to the higher cadence, otherwise your slow twitch fibres are firing too often and will tire. Power is torque times speed, so for the same power you can reduce the torque through your gearing and speed up your cadence, which is something every cyclist with gears will know about. But there is also a limit to what is comfortable and efficient to spin faster – foot distance coupled with leg length and leg mass; consider what 200mm cranks at 100rpm would feel like compared with 150mm at 100rpm. This is why shorter cranks geared correctly are better for you.
