Thank you for looking into it.
Just an idea ... could it perhaps have something to do with differing definitions of intensity? I.e. they seem to be referring to intensity as the amount of 'energy' passing through a given area per second (power per metre squared - consider the units of intensity, Wm-2), whereas I, and other textbooks, have interpreted intensity to be the number of photons per second?
My mind is actually functioning properly now that I'm fully awake and not sleep deprived.
Firstly that answer is most definitely wrong. Your are right, its due to their definition of intensity. I'll explain to you what their answer means and why its wrong. Even though its wrong, developing an understanding is crucial.
Okay so this is the justification of their answer:We have E = hf for each photon. If the light contains 'n' photons, it must carry energy E = nhf. Now this is where they make their crucial mistake. There are two types of Particle physics, Classical and Quantum. In classical Physics the intensity of a wave as you said is defined by W/m^2. Using this definition we can clearly see Intensity is proportional to the Energy of a wave which is E = nhf. So if Intensity stays constant, E must stay constant. However h is a constant, so the only way to keep E constant with an increasing f is by decreasing n.
So now we have that the number of photons decrease.
I hope you can see why this spells trouble, because in Quantum Physics decreasing the number of Photons decreases the intensity of the wave, but lets carry on. So photons decrease, meaning the rate of arrival for the photons will decrease. Which means the photo-current will decrease.
However as I mentioned above this is problematic.The real definition of intensity in this case is proportional to the amount of photons, so 'n' must stay constant in the equation E = nhf. This means the energy of the light wave and subsequently each photon increases. This means each photon carries greater kinetic energy as I mentioned. However now that I'm not half asleep there is something more important to consider.
Greater kinetic energy per photon means each ejected electron will travel a greater distance before the next one is ejected. This effect should more or less cancel out the fact that they are travelling faster. This will lead to basically a constant current, or one that increases just slightly... It wont increase by a lot as I said in my first post.