... 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.[/b] 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.
The pool creates a coinbase entry assigning the block reward to itself.