The nonce you are hashing is done against many things, one of them is the coinbase transaction which must be in the block header, that transaction ensures the payout goes to the pool address, if you change anything in that transaction the hash you sumbit will be invalid to both the pool and the network as a whole.
The pool keeps all necessary data about block header and transactions for a valid submit to bitcoin network and miners are not given all data by the pool. So only the pool can submit solved block header which includes nonce. Transaction data, sometime, is a huge data; so it won't be given to miners in stratum mode. This answers your curious or doubt.
Mining on self node in BTC network has a fundamental good point is that a BTC is going to your BTC address, which can avoid a risk of operation failure in pool side or dishonourable operator of pools. So solo miner must bear this in mind.
Does this mean that the operator of a solo pool has the technical possibility of manipulation, e.g. to redirect the reward to himself in case of a block find? And this although the user of his pool had entered his own Bitcoin address as user name when started the mining? I would be interested from a technical point of view whether this would be possible in general. That would be disastrous, of course, because a pool operator could be a scammer. Can you please explain this in more detail? Thanks.
Yes. solo pool operators can manipulation of your submits and rippe off you at current start of the art in software of the pool side, eg:
1. Pool can submit your found in a different bitcoin address to the bitcoin network. Because the pool got the coinbase data. This is quite wide practice in altercoin pools in terms of my watching. Some pool operators are gangs and untracable, even by Agents.
2. Current miner softwares only got a message indicates the pool accepted this submit. But it does not provide information whether this submit has beem submit to the bitcoin network? or whether bitcoin network has accepted this submit? or confirmed this submit? This is an issue which give the pool operators a back door, I believe. The altercoin pools and miner programs even got worst, they don't provide the height information of block. You never know your submits are accepted by the network or not. They got webpage only indicate few second ago you did submit a share.
3. After you submit your found to the pool, the pool firstly verify your submit with pool's share difficulty and then pool verify your submit with bitcoin network's difficulty. But, the pool never return a feedback information whether your submit is above the network's difficulty. This can be done easily in software, and this is a key issue in transparency of bitcoin network. Actually, the bitcoin core will return a message "under diff, sth like" if submit is below the diff.
So, there is a real risk in crypto coin mining business. When you ran a miner for one year, and got a good submit, then, ripped off or missed.
What can you do? You have to work with reliable pool operator at first place.