Good question. It actually doesn't have to be symmetric, it just has to be distributed in such a way that a random sample will not give you a biased return. (A symmetric distribution is sufficient but not necessary.) The reason this has to be the case is that if a random portfolio gave you a biased return, then the sum of random portfolios would give you a biased return. But the limit of the sum of random portfolios is the whole market, and that can't be biased.
Perhaps it's easier to see from the other side: the monkey is getting the same expected returns as "buy one of everything on your list," but the index fund is not, because the index fund is employing a different weighting strategy (e.g. buy the 30 or 500 largest companies). Of course, if you define "market" using the same list that an index fund uses, the monkey's expected performance converges with that of the index fund.
