That's a good question. I guess that there would be many competitors who'd one make a more generous offer to the miners than the other. They could reach paying half the reward to the miner, just to ensure that their transaction will become valid and not the others'.
Even if they have such connection,
1. The chance of such transaction become valid depends on pool hashrate.
2. There's delay to send RAW transaction and pool operator include it manually, unless they have tool to add specific transaction automatically.
And I have a feeling there are machines watching the mempool for these keys.
Such machine/bot already running since some years ago.
The funds were swept out instantly, which strongly suggests it was a theft by a bot watching that privkey. The passphrase is a song title, wit
Yes, there are a couple of bots active which monitor the mempool (using a modified bitcoind client) for incoming transactions. Each address found is then matched against a very large set of addresses composed on all kinds of brainwallets. In other words: Just because the brainwallet "Jack" hasn't been used yet doesn't mean it is a safe brainwallet. When you would deposit some coins into the attached address you can be sure they will be stolen within the blink of an eye.