The SSA Spokesman Is an Idiot!
I used to work for a pension plan and every year we would purge dozens of pension recipients whose deaths were unreported. And every year we would have to take legal action to recover payments made after death from various parties who "forgot" to report the deaths to us. Multiply our dozens by a thousand (or more) and you can see that overpayments after death should be a major concern for the SSA administration and anybody worried about the financial health of the SSA.