I'll zoom out a bit and first answer the question of why have any private funding requirement at all? We do this not because we don't like government space exploration--we do--but because we want to find a way to make sure that X PRIZE-winning technologies and capabilities are economically sustainable. As great as Apollo and the Soviet programs of the same days were, their tragic flaw was that they couldn't be sustained and that they didn't lead to long-lasting lunar exploration. Government space agency expenditures are often driven by non-repeatable motivations (a particular coalition of power, a need to demonstrate national prestige, et cetera). We can't exactly write in a rule saying "be financially sustainable," so we try to achieve that goal by proxy by saying "raise most of your money from the private market."
With that goal in mind, we could probably make the case for private financing requirements anywhere between 51% and 100%. Traditionally, we've gone with 90% because we think it fulfills our goals, but leaves some flexibility so that we are not ruling out worthy competitors. We don't want a really good team to be turned away because, for example, they won a small SBIR grant a few years ago--and we don't want the controversy of people fighting over what does and does not count.
90% rules have some precedent in things like amateur photography contests, global sporting events, et cetera. We've borrowed from that. Notably, other numbers have been in active discussion for the Google Lunar X PRIZE and other competitions, but the underlying intention and rationale are always the same.