Boy, I muddled that last question. It should have read "does the security to prevent this ...". I guess what I'm asking is if the work you send to my computer is any different than the work my own bitcoin server would send to me. I'm guessing so.
If not, I was assuming that the security scheme for assigning the block to the miner must lie somewhere on my PC and could have interfered with my own mining. I'm hoping a bunch of people jump on here and say, "No way. You just don't understand how it works."
Hey, sorry, but I completely don't understand what's your question...? When you want to solve blocks standalone, simply connect your miner to your local bitcoind.
Several days ago I hit upon a block while mining on my own and it did not go through.
It is sometimes possible, you can find a block, but anybody else (maybe the pool :-) send valid block just a second before your own solution. Then your block is not counted...
I like pooled mining, but I'd also like to try again on my own and I began to wonder whether the pooled mining had somehow gotten in the way of mining
If you connect your miner directly to own bitcoind, there is no way how can pool interfere with your mining effort. (if this is core of your question)