F means there is not legal way for a private citizen to own it, AAA Corp Sec forces on said corps property ARE the Army. What is and is not F changes by Corp and Local jurisdiction when not on AAA corp property. So Yes KE guys can run around with all kinds of F rated gear with no problems.
Again, yes and no.
First, we seem to be saying the same thing in terms of jurisdiction. However, there are really multiple levels of F that the game doesn't differentiate between for practical reasons. Yes, Ares can kit their guys out with mustard gas, but whether they're in the Barrens or the Desert Wars, it's still "illegal" (assuming the Geneva Accords are still in place), even if the accountability will be more focused on holding Ares accountable rather than the security guards. Additionally, even if your guard is KE on Ares turf, he probably should still stay away from Bliss, for example.
Second, security guards are not going to have the same leeway everywhere. When we talk about "security guards" in the abstract, it can be KE on an Ares site or the Red Samurai at Renraku, but it might also be Lone Star or Wolverine (bub).
Being part of a security team, or another government/megacorporate team, does not guarantee you access to F gear. It's going to be a GM call on a case by case basis.