In a pooled mining situation, the winning hash cannot be used as "your own".

The hash incorporates all of the transactions in the block, including the one that pays 50 BTC to the generator.

If you are hashing for pooled generation, the winning hash is only useful to the pool.

If you are hashing for yourself, then obviously the winning hash is useful to you. But in that case the "low-difficulty" hashes that you generate are useless to the pool, so the pool will not pay you a share of the generated 50 BTC.

It is a solved problem to prevent cheating with pooled generation.