These types of things are fairly common when random number generating algorithms are involved. Basically, computers cannot really generate truly random numbers, you would need a decaying radioisotope to do that. If you are doing something like Monte Carlo approximations, for example, it can be pretty important what algorithm you use, since it could increase the uncertainty of your calculation if you use one that has results that deviate from a perfectly random probability distribution (uniform distribution for Brawl purposes, I think). The Wii probably uses a very simple algorithm or maybe even stored sets of random numbers to output (probably to increase performance), so that is probably what is causing these seemingly nonrandom results.
There is also observer bias. You will pay more attention to results that do not happen often, because you were not expecting them, but the results can still be consistant with the (uniform) distribution of values we expect. To prove that something is random or not with confidence you would need more way samples. Unless someone wants to run detailed experiments and calculate the p values to prove otherwise, we can assume that these things are done based on a random number generated by the Wii.
/thread?