FBI was pretty worthless.
Every plan or idea they had failed and was wrong. And every time Mullin flipped the script and did what they didn't want him to do, it worked.
The FBI wanted him to just pay the ransom, because most of the time those parents get their kids back alive. Mullin was smart to realize that these people would never want his son to come back alive, since he could ID them later, and during the botched drop off the guy he gave the money too had no idea where his son was supposed to be. Even after that, they still wanted him to just pay the money, but Mullin went public and put up the bounty instead. Then they tried to undermined that by sending his wife with the money, and she then gets beaten up. But in the end, Mullin's plan worked. The kidnappers panicked and turned on each other, and he got his kid back.