I am not so sure if the FBI hat has a special meaning related to the hoax. It is not uncommon to see people in the US wear hats that feature FBI, CIA or military such as Army, Navy etc. This trend picked up even more after September 11th. Everywhere you turned there were NYPD and NYFD hats.
I found the shirts that Jermaine and Jackie wore during the reality series to be more intriguing. One wore a shirt with Bahrain on it and the other brother wore a shirt with Ireland on it. Those were two places where MJ spent a considerable amount of time. I am curious about those shirts moreso than the hat.