Sorry, I only did a little research for this section (and that was a week ago), so I might be a bit confused.

If I understand correctly, anyone who joins a pool (excepting p2pool) gets zero mining-related information from their own `bitcoind`.  So, in my mind, pools and non-full-node workers are related and p2pool is a special exception.

Is my understanding correct?  Is it the idea that p2pool is a special exception what you're arguing against---do you think that it's actually a third case?  (Solo, pool, p2pool)