The article isn't claiming that faster speed == safer. It clearly states that raising the speed limit has little effect on the speed that most people travel. The only group of people whose driving speed it significantly affects is the 10% of people who follow the speed limit exactly (who are usually the slowest drivers). Therefore, by raising the speed limit, a large majority of drivers will drive at the same speed (no faster), but the slowest drivers will speed up and the speed differential drops, making the roads safer, as your linked article agrees with.
There was little evidence presented that justified the assumption that most people won't drive any faster with a raised speed limit, but if we take that as true, then its conclusion is consistent with the research you linked. It is NOT making the claim that driving faster is safer. In fact, it again clearly states that in an ideal world, everybody would just travel at slower and safer speeds, but that we can't effectively enforce such a low speed limit.