Reminds me of a seasoned professor of Quantum Chem that I know, who confided that it took him quite a few years before he figured out why chemists insisted on using pKa as a measure of acid/base strength. Which was understandable; Coming from a physics background, he'd naturally never done a titration in his life. From his physical/theoretical viewpoint, the most natural measure of acidity is proton affinity. That is, the total energy (in vacuum) of the molecule with a proton, minus the total energy of the molecule without a proton.
It's a simple and precise definition but useless to the chemist, since it doesn't directly correspond to anything you can measure. Theoretically, calculating proton affinities is fairly easy, but calculating pKa is actually quite hard. The equillibrium constant is related to deltaG for the dissociation reaction. That deltaG is only weakly related to the proton affinity energy. To begin with, both the molecule and proton are in solution. Second, you have the electrostatic/Nernst potential from the protons already in solution, and the mixing entropy/concentration, and the whole difficulty of figuring out what the entropy of a dissolved proton in water really is. Theoretically it's a rather hairy concept, and a good amount of effort has gone into figuring out ways to calculate pKa.
So that's a bit of trivia for you: deltaG has a certain concentration dependence. Actually it always does, but it's larger for acid/base reactions since concentration changes also change the ionic strength, etc. So Kb itself also has a certain concentration dependence.
As for the question, it depends on what they were asking. pOH, like pH is by definition a concentration, and it's the measure of acidity of a solution. You could call it the 'strength' of the solution's acidity/alkalinity if you like. But it's certainly not a measure of the strength of an acid or base itself, no.
How could it be? In the simplest possible terms: How could you tell from pH alone whether you've got a high concentration of a weak acid or a low concentration of a strong acid? What you would need then, is the concentration of H+ or OH- relative the amount of acid/base: Which is essentially what pKa is!
