Recent "the sky is falling" news stories have dealt with the fall from orbit of the Mir Space Station rather than NEO impacts. The press and public are clearly interested in the risk of falling objects, but sometimes risks are perceived in ways that are quite different from the hazard as calculated numerically. The following is a very rough estimate of risks, in "order of magnitude" terms only. It is intended to be illustrative, but certainly not precise. By risk I mean the chance or probability that any individual will be killed as a result of either a spacecraft atmospheric entry or the impact of a NEO.
Let's start with the risk of death as a result of being struck by a piece of Mir on the assumption that the fragments could land anywhere on Earth. Suppose 1000 large metal fragments survive to hit the ground, and that if you are within 1 meter of the impact point you will be killed. Thus 1000 square meters are at risk, out of a total surface area of the Earth of about 100 trillion (10**14) square meters (not counting the Polar Regions). This is one part in 100 billion of the Earth's surface, and that is the risk to each individual. Multiplying by the Earth's population of 6 billion, we get a chance of about 1 in 20 that one person on Earth would be killed.
In fact, the Mir atmospheric entry was far from random. It was steered to an impact point in the mid-Pacific Ocean. Unless you lived in that part of the world, the risk to you was zero (not allowing for an uncertainty in how well this controlled entry would be executed). Since the total population of the Pacific is only a few million, the chance that someone would be killed was less than 1 in 20,000. The folks who sold the Russians a $200 million insurance policy were very unlikely to have to pay off any claims.
For comparison, consider the annual risk of dying as a result of an NEO collision with the Earth. A number of studies (e.g., the paper that Clark Chapman and I published in Nature in 1994) have shown that this risk is dominated by near Earth asteroids of about 2 km diameter. There is a roughly 1 in a million chance of such an impact each year, with estimated death of 1-2 billion people. Thus the annual risk to each of us of from NEO impacts is about 1 in a few million, or more than 10,000 times greater than the risk from an uncontrolled Mir entry. (Note: This is a conservative estimate; many would argue for a NEO-impact risk that is higher by an order of magnitude.)
We see from these simple calculations that the risk (per year) to each of us from asteroid impact is thousands of times greater than from an uncontrolled Mir entry, and millions of times greater than from a controlled Mir dive into the Pacific. Yet no one is taking out insurance policies to protect from cosmic impacts, and this risk receives less news coverage than the demise of Mir. Why the disparity? For one thing, the death of Mir was a known event that provided a good story, while we have no specific prediction of any NEO impact. For another, Mir was a human-built object over which we had some control (and responsibility), while an NEO impact is considered an "act of God". But I suspect that the difference also reflects the fact that very few reporters tried to make a quantitative comparison of these risks. If they had, the results might have surprised them!