Why I do not think The Hunger Games is a ripoff of this.
As an aspiring writer who knows many other writers (both aspiring and published), I can tell you all of us have had "original" ideas only to find out later some people had written about them before. When Collins says she got the idea for The Hunger Games watching both war and reality shows in TV, and added the tributes from the mythological story of Theseus and the Minotaur, I do believe her. I had lots of ideas that were used before I could write them by authors like Asimov and George R.R. Martin. All my friends who write (some of them published already) complain about the "Oh, no, I did the "unknown plagiarism again"! " It sucks when you come up with what you think is a great idea and you find out that someone used it before. My alien race with three sexes? Asimov did it before, damnit. My two deconstructions of the fantasy princess, the Disneyesque and the warrior princess? Sansa and Arya Stark. A friend of mine (already published her first novel, not in English) had the idea of the wolf who became man during nights of full moon. Done in the 18th century by some French dude. Then she had this great idea for her steampunk novel where people paid with time and not money. When she was told about "In Time", she was really depressed. (By the way, I told her she should go on with her novel because "In Time" totally wasted such a great premise: even if no one believes she had the idea on her own, that's unimportant, I believe she could do a better job with it). Another writer of my acquaintance (second novel published and working on the third) has had this happen to her.
It is VERY difficult to find an idea that hasn't been written about before by someone, somewhere in the world even if the idea came naturally to you. Of course, no one is going to believe you... except for other writers. I do believe a writer when he or she says he had the idea before or the idea came from other source, because it's actually very common whenever you're trying to get ideas. Happens all the time.
To Collins' credit I must add Battle Royale wasn't exactly a very well-known movie before The Hunger Games appeared. I am a Japanophile who reads manga and watches anime, and even listens to j-pop and j-rock, and I found the movie out of coincidence. It's not mainstream famous, so I think Collins' version is believable (if you are a writer or someone who's ever had an idea for a story: if you completely believe that two people in different places and times cannot EVER have the same idea or a similar one, then of course you'll think Collins did a ripoff).
If I thought Collins was ripping off, I would rather go for something like "The Running Man", the movie. The Hunger Games has much more of the brutal, ruthless TV show vibe, than it has of Battle Royale. So, if anything, I would think Collins got inspiration from "The Running Man" and then gave the other version: she was watching war in TV, and a reality show, had the idea of blending them, and added the idea of tributes from the mythological story of Theseus and the Minotaur. By the way, I know it may seem "too much of a coincidence" that two lovers survive from both Hunger Games and Battle Royale. The problem is that in the Story of Theseus and the Minotaur, both Theseus and Ariadna do survive after killing the Minotaur and get away with it. So I don't think Collins' story is that far-fetched. She could be lying, of course, but she could perfectly be telling the truth.
That said: originality died with Shakespeare, and he killed it (most of his plays were based on other people's or prior stories and legends: it's only that his own were remembered best).
Again, that said: even if Collins had copied the basic premise from Battle Royale, The Hunger Games still deserves to exist and stands on its own. And The Hunger Games will probably always be the best remake you can do of Battle Royale for the Western world. For starters, Battle Royale criticises the brutally competitive system of education and job market of Japan. It is great at doing that, but you cannot apply that to the Western world. I am from Spain and we only have trouble at 20% unemployment rate: 15% unemployment rate here would be good news.
However, The Hunger Games criticises (and is a metaphor for) other flaws of Western society. How the rich parts has incredible technology and wastes food and resources in entertainment while the poorest zones or poorest countries are getting their resources basically stolen or exploited. How the population is idiotized by sensationalistic media. The brutal sensationalization and publicizing of people's suffering is hit spot on by The Hunger Games, with its glamourization of what's going to be a deadly gladiatorial combat.
I think both stories are very deserving, and both very needed. Both are metaphors for problems of the societies they represent. As for me, I can believe Collins came up with the idea for the Hunger Games of her own: gladiatorial games existed before Battle Royale came out. If she didn't she still made a very good trilogy, that addresses completely different topics from the ones treated on Battle Royale.
One of the main points of Battle Royale is that the combatants are children, unexperienced in violence and unable to fend for themselves. That's absolutely NOT the case with Katniss Everdeen and most of the people she faces. Katniss is a survivor, the sole breadwinner in her family from age 12, hardened by experience and certainly more than willing to kill once the games start. When Collins was asked about the actress that should play Katniss, she said she didn't mind that Lawrence was 20, because according to her "better an adult-looking actress than a younger one". The most poignant thing about Battle Royale is how young the kids look: they look innocent and a bit spoilt, they are clueless and helpless and cannot manage on their own. Katniss is a trained hunter and survivor, and even the baker kid can strangle people with his bare arms. The other children are killed, but their innocence remains intact. You don't see in THG the "Lord of the Flies" psychological destruction that is probably the saddest part of Battle Royale.
It bears mention that The Hunger Games has very defined good and evil characters. Again, in The Hunger Games, the innocent children die as innocent as they got into the arena. The fighters fight, the evil ones remain evil. Battle Royale participants not only lose their lives and limbs: they are psychologically affected by the competition (and that destruction is again, the cruelest part of the Battle).
If you scratch the superficial similarities, Battle Royale is a metaphor for the brutal competitive streak of Japanese High School system and job market. The Hunger Games is a metaphor for how the rich parts of the world live in comparison with poorer countries, and how idiotized the population of said rich countries are.
The comparisons with Battle Royale may hold for book 1. Books 2 and 3 tell a completely different story. Book 2 is quite different, and book 3 bears absolutely no resemblance to Battle Royale whatsoever.
I always thought a "ripoff" had to be something really, really similar to the "ripped off" idea. Maybe it's because I consider "The Hunger Games" a trilogy and I know it complete, but I don't see the ripoff. I can see a similar starting premise, but the story deviates so much, and the premise is so differently treated, that I really think the comparisons make no sense. Once everyone is finished, the stories are very, very different, the characters have little to do with each other, and their development is completely different in both movies.
So, similar premise? Yes, sure. Rip-off? No.