This rule was added due to a discussion on Clever bounty reputation hack (on Meta SE) back in 2010.
So here's the hack:
Find an interesting question
Research and provide a very good answer
Open up a bounty on that question to attract attention and votes to your new answer
2 and 3 may be out of order--I didn't see the timing ...
The bounty amount is deducted from your reputation when the bounty starts, not when it's awarded. For the particular example you mentioned, you can see exactly what happened on the reputation tab of that user's profile. They started with 1 like everyone else, got +100 of association bonus, and then spent it on the bounty to get back to 1 rep. They also got ...
You cannot currently offer a second bounty on that question because you do not have enough reputation to do so.
The minimum bounty amount doubles on each subsequent bounty you offer on a question:
Additionally, if you offer multiple bounties on the same question, the minimum spend doubles with each subsequent bounty (50 reputation on the first bounty, ...