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.