Bitcoins mined by the pool are generated by the pool. Shares of the block reward are sent by the pool to miners just like any other transaction.
Is it save to say that these warnings/statement by the Exhanges are ment for solo miners and pools them selves?
No, Eligius and P2pool pay participants using a different way than most other pools, that technically behaves like solo mining. The payouts are performed in the coinbase transaction in blocks they mine.
Exactly, they put the miners' address directly in the coinbase tx.
I don't really understand why people still use the exchange deposit addresses to collect P2Pool payment when the exchanges explicit ask you not to do so.