It's a good thing in this case they also don't have to worry too much about bad actors, since it's a fundamentally altruistic endeavor. Worst case scenarios:

1) Someone keeps downloading the full archive and throwing away;

2) Someone wants a file erased, keeping it with the intention of denying access in some future.

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1) Bandwidth has costs on both sides; just balancing upload among receivers would probably suffice for this not to be a problem.

2) Assigning large random chunks to downloaders should prevent this "chosen-block attack"; add in some global redundancy for good measure and that's probably enough (although I still wouldn't trust this 100% as a primary storage, only as an insurance storage).