Do you agree that the lowest number of new unemployment claims in 4 years indicates a U.S. economic recovery?

It seems that all of the U.S. media from Fox to N.P.R. are celebrating the relatively low number of new unemployment claims as good news and a sign that our economy is recovering, but can anyone explain to me how a drop in new unemployment claims tells us anything at all about the overall health of our economy?

Say, hypothetically, that you live in a nation with 200 million workers and in 1 month 100 million of them, or half of your workforce, are fired and file for unemployment. Then, in the next month 75 million more are fired and file for unemployment. The new unemployment claims just went down by 25% but you lost 75% of your remaining workforce.

Or, to put it another way, imagine that every worker in the U.S. got fired and all of those that could file for unemployment did so. A month or two later the new unemployment claims would drop to zero because there would be no one left to fire and no one who could file new claims.

Would that be good news?

Or are we being fed poop and told it's pudding?