I can't personally imagine carrying ANY gun outside of a holster, but then I view the holster as part of a complete "safety process" I apply to my guns. If a handgun is loaded with one in the chamber, it's in a holster whether the holster is on my body or not. It's a message to me and to my 21 year old son that lives with me, that it's loaded. It's the house rule.
As far as the PT111, since it's a DA only with safety and loaded chamber indicator I suppose one could argue that would be safer outside of a holster than a Glock or Sig. I'll admit I don't use the type of holster I use for the rest of the guns I carry, just a simple cloth type from Uncle Mike's ($14) COB, but it's still in a holster if for no other reason than consistency and to keep it clean from sweat, dirt and body oils.