I find it implausible. There's got to be more to it than the OP is letting on. When I was 18, I got arrested for theft. My friend and I stole $11 worth of gas from a convenience store and drove off.
Since that time, I have passed, and been hired, by three different state and city law enforcement agencies and passed two Federal background checks of which, one was DEA and the other was Border Patrol, when it was was under the jurisdiction of the Department of Justice.
There is no way FedX is more stringent than the Federal Government or state and local law enforcement agencies when it comes to the hiring standards of people with a criminal record.