Yes, I actually quite oppose the idea that they only get eleven months, or so many months, back payment. If they turn 65, they turn 65. What does it matter that they turned 65 eleven months ago or five years ago? They were still entitled to the money. They still have a right. It is not their fault if they did not know about the program.
The government is not promoting the program, or these people would have known about the program, regardless of what government is in power.