Okay I think I've got it - the dividends are funds which aren't explicitly recorded in the blockchain, but which can be inferred by examination of the blockchain. The cleanest implementation I can think of would be to add them as coinbase transactions that are immediately spendable and spent in the block in which they are added. Conceptually, it's very clean, but implementation would require very careful work. You'd have to be extra careful to avoid ruling out the possibility of a lightweight client in the future.