Consider this situation... This is hypothetical but entirely possible, and *every intersection and driving situation is different in some way*, so please don't be so quick to judge with limited knowledge of what actually happened. It's entirely possible to do everything right and still get into an accident.
Hypothetical situation:
The side that is covered in snow has a red light, and the cross traffic has a green light. Perhaps this is at an intersection where the traffic lights were installed specifically because it is a difficult and low-visibility intersection. The traffic with the green light may assume everything is normal with the lights and may be traveling *at full speed*. A car on the "red" side treats it as a 4-way-stop situation, stops at the light, looks and doesn't see any traffic, and then goes. Remember that if it's a limited visibility intersection and the cross traffic is going full speed (and is therefore some distance away from the intersection when the "red" car commits to going through the intersection), it's certainly possible that this driver could not possibly see the other car coming before it's too late. Also consider that it recently snowed (or is still snowing), meaning the road is likely to be extremely slippery. Even after the two cars see each other, the "green" car will have difficulty slowing down sufficiently to avoid hitting the "red" car.
I think this is a fairly realistic and possible situation, and in such a situation, the "green" car that had full visibility to the lights would be more to blame than the "red" car that can't clearly see the lights. Obviously the "green" car would have now real way of knowing something was wrong with the lights on the other side, but in such a situation (recent snow, slippery roads, etc.), they drive slower and more cautiously as they approach intersections.
On your comment about making sure the other guy will yield, it's entirely possible that at the time you're starting to go through the intersection, there might not even be "another guy" to consider until you're already in the middle of the intersection, if the "other guy" is driving at full speed.