I don't know much about Tahoe-LAFS, but if there's no built-in incentive to provide storage, I'm guessing there's also no built in verification that you're actually storing what you say you are.
In Tahoe-LAFS there's a verify-capability associated with each file that lets you do an integrity check over the ciphertext and erasure coded shares for that file. A server can only lie about storing a file until another node attempts to verify it, and this can easily be scheduled to happen periodically.