The main reason this has become an issue has to do with parents not being able to prove the infant is who the infant is.
Let me explain....
If a person on a no fly list buys a ticket as a general rule he can not fly. However, you can buy tickets from a multiple of sites and never need identity to do so. Expedia.come, CheapTickets.com etc etc. The issue is once you get to the airport to check in, your name MAY be flagged depending on how good the system is going for that day.
So lets say Usama Bin Lauden buys a ticket via his personal computer. He makes arrangements with another person to swap tickets. In many cases you can walk right through security with someone else's ticket. Especially if it is busy or if your picture is even remotely close to the issued ticket. So the bad guy walks through fairly easily.
In the mean time, and at the same relative time, (intentionally done this way to create an issue at another security check point, helps take away from the bad guys check point), the person that traded tickets gets stopped. Eventually he/she will be able to get cleared but not until they can prove their identify via 3 forms of ID. Not too many people carry three forms of ID. And in this case they intentionally carry on a single form of ID. It takes time to straighten it out. Long enough normally that the bad guys is through security and in the air...
So it really has nothing to do with the infant so to speak. In a fair amount of cases the other person is nothing but a tool.
There has also been honest cases where names simply match up. In these cases it is treated the same as TSA does not know if it is a rouse, a test or an honest mistake.
I have seen this done. We follow cases like this all to often.