Let's think about boxing. It's not set up as a bloodsport per se. But because of the better culture, it becomes extremely corrupt. Not only that, because blows to the head are not discouraged (well, it involves a knockout, rather than like sumo a simple ringout, and while you could in theory knock someone out through body blows, the results in long term might be internal bleeding), it is easy to over time crush someone brains out. This is a sport with known potential for corruption.
Or football, where 300+ lb guys are encouraged to tackle (pinning would be alot safer) meaning a high-speed impact with 300 lb of weight. These might as well be human cars. To say nothing of also extreme brain injuries because of the extremely hard helmets (what was wrong with leather headgear again? Seriously). This is a sport where there might be corruption, but we would not know about it from the setup.
The audience doesn't think about the lethal aspects of the event, if it's not commonplace. If it is commonplace, they can become desensitized to it. But in the cause that it is rare, there is such a thing as a planned accident.
Let's use football as an example again. Suppose a player was really unpopular, some idealist type that made a lot of changes and upgrades to the sport. The teammates love them, the audience doesn't know about this, and the officials
hate them. Under family-friendly rules, let's say the teams are paid money to arrange a little "accident". Sometime during the 3rd quarter, the player has the ball after being hiked back, and is preparing to throw it. Instead of guarding the player, the team fans out, as if preparing to catch the pass (but in fact, leaving that player completely open) while they figure out who to throw it to. In comes the other team, slamming together against this player. From the audience's perspective, it's a bad play. They don't think "that guy is going home in a body bag."
http://www.theguardian.com/sport/2014/oct/03/american-football-third-us-teenI don't know that it's to that point yet, but still...
So back to the "games". We know that this country, because there are no taxes, everything including basic utilities is run by business. We also know that it is a constitutional anarchy. The games, then, are every bit as corrupt as boxing, and worse, the audience is probably told that the players are healed after every game, and repeatedly told about the penalty (as in, propaganda that the games are safe). Whether people are alive and wounded, or very clearly dead, they are likely walked off the field in much the same way so as the audience sees what they expect to see, not someone killed because they were a trouble maker, but X fighter beat Y in battle, so rather than a bloodfest, they just think of it as an exciting fight.
There is also the fact that there is the "no force" culture. You can conceivably have that, but there are certain side effects, like that some violent drives get pushed into the background and people subconsciously crave things like gore and rape. That is, without reasonable situations where people would fight to defend themselves (think about Bern's original situation, and how she was basically not even allowed to threaten the guy), the outlet for some of their flight or fight hormones manifests in weird ways.
Hopefully, between her dad betting on her, and possibly the warden betting on her, her debt can be paid off. Otherwise, I don't know how she'd hold up in future battles, except against opponents that didn't understand her sword. Hopefully, she can use the downtime to figure out more of what it does.