My understanding is that it is largely an accounting optimization.
Their explanation: http://www.quora.com/What-is-500-Startups-business-model
Important to understand: they've got one brand but two entities, the investment fund and the accelerator. The accelerator is designed to take in $X per year in revenue and pay out $X in expenses, for a net profit of zero or slightly negative. (Having more than slightly negative is tax inefficient. You get to book the implicit tax value of the loss as a carryforward asset but you would have no way to ultimately realize it since the accelerator is designed in this model to never actually make significant amounts of money.)
"But isn't it equivalent if you just give them $75k." No, not equivalent. This manages to teleport revenue through time from the eventual carry into the present, pays for present cash expenses, and gives that revenue favorable tax treatment.
How exactly it's favorable tax treatment is a great question for a tax lawyer. Here's my layman's understanding: you can deduct expenses from capital gains prior to taxing them but they have to have a certain level of connection with the gains, and it is possible that "general administrative expenses of our operation" don't have that level of connection. Shuffling those expenses into the accelerator makes them clearly deductible against the accelerator's ordinary income, since the accelerator looks like any money-comes-in-money-goes-out IT business. The program fee is clearly revenue. Their rent is clearly an expense. If revenues equal expenses than their revenues are taxed at, effectively, 0%.
"Tax optimization on $25k doesn't make sense" would be a sensible objection until you remember that 500 Startups operates at industrial scale and that this is suddenly $3 million in revenue a year.
n.b. 500 Startups would, eventually, pay whatever the normal capital gains taxes are on the carry (and/or ordinary income tax if the law is ever changed to make it less favorable), in accordance with the standard treatment of investments under US tax law. It's not an avoidance strategy, it is a temporal optimization strategy.
Edit to add: Above explanation is purely "My best understanding of the matter as someone who had no hand in putting this together." based on my inexpert understanding of standard US principles of taxation and their public statements about it.