Ah. The hashing info is calculated taking into account the payout address?
The mining reward payout is just another transaction. Therefore it affects what the merkle root looks like.
When someone is mining, do they add the transaction that pays them out to the blockchain they have, changing the merkleroot, and then hash it and broadcast it? This way someone can not change where the payout goes to without rehashing/doing a crapton of work.
Miners collect transactions they've received from other nodes and verified as valid based on their version of the blockchain. They add to this set a transaction paying 25 BTC (right now) plus the amount of fees from the set of transactions collected, to an address of their choosing. The hash of the merkle root is calculated using this set of transaction. This merkle root hash is added into the header for a yet-to-be-mined block and the miner then starts to try and find a nonce-value that, when added to the block header, produces a block-header-hash that meets the requirements. If new transactions come in, the hash of the merkle root is recalculated and mining is resumed with the new data.
Once this happens, the miner broadcasts the entire block to the network and other nodes add the block to their local copy of the blockchain. At this point, anyone wanting to change the payout address of the mining reward, has to alter this transaction, recalculate the merkle root and try and find a suitable nonce (= redo the mining process for this block). All the while competing with legit nodes receiving the unaltered block and starting work on the next block.