Well, I'm an insurance lawyer in Australia, so neither the law nor the benefits schemes are identical, but here's the principle:
If, e.g., you are injured by someone else's fault, and can't work, you have to give up work and go on a disability pension. That's government benefits paid to support people who can't work by reason of health, right?
So then you sue the wrongdoer, and they pay you a lump sum of compensation. What they are compensating you for is the fact that you have lost all that money in medical expenses and lost income due to the injury. Compensation is exactly that; it's not a way to say sorry, it's there to compensate for actual material loss.
So then the government says, well now you've been paid twice. First we paid your medical expenses and salary, and now the wrongdoer has paid it again, you can't get it twice, we want our bit back. So they take their bit back.
Compensation at common law exceeds benefits, though, so you usually end up with some leftover. Not always, to be honest; I've seen longrunning cases, where by the time the Medical Expense Benefit people and the Income Support Benefit people (I'm making up the nameS) are both paid back, there's nothing left for the plaintiff.
But that's the principle. Can't be paid twice.