For those who wondered how the Match works, the algorithm is briefly explained here, with links to more detailed explanations. (So whoever wrote that if you don't get your first choice, it's randomly assigned from the subsequent choices, that's just wrong. As I thought.)
I also read (somewhere) that when they first started using the Match system, the algorithm began with the preferences of the internship sites. People (interns, probably) complained that this gave sites a power advantage, so they tried out the current system, beginning with applicant preferences. Although this showed less than a tenth of a percent difference in placements when applied to previous Match years, they decided to adopt that system anyway.