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After reaching a minimum payout limit ,you will be asked for the bitcoin address to which the coins are directly sent from the website .So not sending enough coins to the block chain does make sense when your payout amounts are lower than the tx fees.
They ask to add bitcoin address before you can make any retweet and after than if you have lower amount of followers they just say payout is very small amount so can't be sent on blockchain.
actually found they have listed this question in their faq page here
https://birds.bitcoin.com/about two times
Sponsors set payouts per 100 Twitter followers. If you have less than 100 Twitter followers the reward for retweeting may be too low to be sent to the blockchain. This means that the transaction fees required for sending the transaction to the blockchain are higher than the reward you would receive for retweeting. If you gain more Twitter followers then the amount you would be rewarded for retweeting any given message will increase; once you reach a number of followers that will grant you a sufficient reward you will be able to retweet the message.
However reward amount look quite confusing as some even have 7750 bits in reward (don't know for how much followers) but i don't think a transaction with 7750 bits can be considered as dust payment. I think they are still working on this issue, and may come up with some solution or answer.
