The company doesn't care about punishing you, it's statistics. The insurance company is taking a gamble, and the odds of being in another accident, given that you've already been in an accident, are much higher than they were before. The odds have tipped against the insurance company, so they charge you more to keep it worth their while.
If you are not at fault, you are not at fault. If they could get away with pinning the blame on the other guy they surely would. So they have 0 legitimate reason to assume that your chances of being in another accident are higher than before, let alone 'much' higher.
The legal--or even common--definition of "fault" isn't at stake here. The fact of the matter is that they've got mountains of data that say that if some "random crazy fluke thing" happened to you, then you're more likely to have it happen again. Because that's what the data tells them. Heck, it could be that you just live in an area where people drive like crap.
Look at it this way: let's pretend an accident (regardless of fault) actually lowered the chances of a subsequent accident (maybe you're scared into good driving), and the longer you drove without an accident, the more likely you are to have one (maybe you become complacent or something). In this situation, your rates would go down when you got in an accident. Because it's not that they're trying to punish you, but rather they're trying to just charge based on the X% chance you're going to be in an accident, plus Y% overhead/profit.
