First, he certainly made a clear challenge, an offer. If I do X, he will pay me Y. If you don't want to call it a bet, that's fine. But that offer would be as legally binding as any other, like "if you work for an hour, I'll pay you $10."
You're being pedantic. You've taken a casual statement and trying to turn it into a legally binding offer. If you really wanted to take him up on that, the intelligent thing to do would be to ask him to confirm the sincerity of the offer. His "offer" lacked any specifics whatsoever so it is hard to take it seriously as "legally binding". You didn't bet anything in return. You just jumped on it and said "Gotcha! Pay up!".
Second, sure anyone can buy lots of tickets to stack the odds in their favor. But the lottery owner had the distinct advantage of being able to take the money, win or lose, unless it's in trusted escrow. So, no, it's incorrect to say that "anyone can do it", because the lottery owner has a HUGE advantage that no one else has. He can take cash, win or lose.
The lottery owner can take the money at any time, if he chooses to be dishonest. But that has nothing to do with buying tickets. You continue to try to tie buying tickets with cheating. The lottery owner, if he chooses to buy tickets, has no advantage over other ticket buyers, since the block explorer makes all bets public and the method for choosing a winner is pre-determined and verifiable.
If the owner of Mt. Gox wanted to run off with all of the money and bitcoins he has been entrusted with, he could do so at any time. If the operator of any of the public mining pools wanted to suddenly stop paying out and run off with the mined bitcoins, he could do so at any time. It would be criminal, and it would be obvious.
Finally, your third premise, that it would be obvious to all, if he ran off with the money, this is true,
Thank you for confirming that you did not win the supposed bet.
but my point is that such an unscrupulous lottery owner would be cheating everyone on the transactions where he wins. What you call aggressive betting, I call "can't lose" betting.
Like I have said before, he may have bought 130 of the 131 tickets in the June lotto, and you can't prove to me otherwise. And if he did, that's more than "aggressive betting". It's cheating some people out of 1 BTC.
First of all, you are the one making an accusation that he "may have" bought 130 tickets, it is your job to prove your claim, not anyone else's job to disprove it. Block explorer is out there for anyone to view. Why don't you go and look at all of the bets that were made last month and try to connect some of them together?
Second, suppose he did. Out of 131 tickets, he bought 130. That would mean only one other person spent any bitcoins. So he paid himself 130 bitcoins to win 1 bitcoin. Even if you accept that this is cheating, in this scenario he has only cheating *one* person out of *one* bitcoin.
What you are suggesting is that a lottery operator could bet 130 bitcoins in order to win 1 bitcoin. While it may be possible, it would be a very dumb bet. Nor does it seem like a scenario worth worrying about. I'd be much more concerned about the pool operators and exchange operators, who are dealing with much larger sums of money, and don't need to outpay their customers 99 to 1 in order to pull off a fraud.