If you think "that who gets the reward for a block, and who "solves" it are two different questions", then I am certain you do not comprehend that even in pool "mining" there must be an entity to receive the reward, what is not the pool participant. The reward needs to be transmitted (first transaction) to the entity which "solves" the block. You are failing to understand that the receiver (thus the "solver") it is not the pool participant.
That is not a correct statement. p2pool and eligius are evidence of that.
, that solution is transmitted along with the filled-in coinbase. Once accepted onto the blockchain, the mined BTC and fees are sent to the address that the pool assigned as the receiver in their coinbase entry.
if you are solo mining, you are creating a coinbase with your own wallet ID in it specifying where the reward goes (into your wallet) when you submit a block solution.
P2Pool and Eligius don't do that. The coinbase transaction has outputs for every miner that will get paid, and a share of the payment goes to each miner as a 'mined' transaction.
The piece highlighted in green is the part Mr. Augusto Croppo refuses to understand. He is trying to redefine "solving" a block as receiving the block reward, which to any reasonable person is clearly a different thing. It is analogous to redefining 'work' as 'getting a paycheck'. One would hope that the latter would accompany the former, but it is clearly inaccurate to say they are the same thing.