Memorization of the correct and incorrect answers is all that is needed for the described (too small of a sample size to be considered an) "experiment".
How far /. has fallen...
It is true that memorisation could explain this. You point about the sample size is trickier, though. Firstly there is no magic number that constitutes a large (vs small) sample size. What is suitable depends on the size of the effect, the variance, and the degree to which you want to generalise the results to a wider population. This is often balanced against what is possible. In biology a lot of experiments have a small sample size because of the cost or difficulty in gathering the data. For instance, I just reviewed a paper where the authors have gathered data from just a single subject. However, they gather a vast amount and do a very thorough job. Their work still stands as it is (it's in a sense a methods paper) and given that they aren't targetting a big name journal or over-selling their results I'm going to let the n=1 slide.
In the particular case of this paper, what I find most annoying isn't the n=14 but that their graphs hide the underlying data by displaying them as just bars with a 95% confidence interval for the mean. I would also agree, however, that I don't see why in this case they couldn't have produced a larger sample size. That's not the main issue, IMHO, however.