Your first couple posts really paint the picture from the Post Office's viewpoint -- And you know the dog and the situation . . . Imagine how a stranger might describe the same event.
You said the dog sounded like it would tear you apart. I'm guessing that includes some lunging against the door too.
You said that no way would the dog let someone into the house. In other words, it must be a VERY ferocious sounding dog. In fact, it sounds like it would actually bite if "it wouldn't let someone in the house."
If the dog is that scary, no one is going to walk up to the mailbox everyday terrified that the door isn't latched properly. (I don't think you've mentioned what breed it is, but if it's one of the recognized "vicious" "dangerous" breeds, that adds another layer of credibility to the postal carrier's fears.) It doesn't matter that it's behind a screen door or a mesh door. (I know of one instance where a mastiff came through a picture window. I don't think it was actually going to bite anyone, but it was just a loud wild dog and slammed up against the glass one too many times. Took a lot of stitches and made a lot of mess. Just "being inside" might not always be enough.)
(Side story -- Reminds me of a private zoo at a resort I stayed at. They had everything, but the tigers were right outside the townhouse I was staying in -- just across the sidewalk from where I parked my car. I was standing there watching this big male tiger pace back-and-forth, looking back at me, on the other side of some heavy chain-link fence. After a couple seconds I broke eye contact and backed away and got in my car! I remember thinking "this is nuts!")
With all the lawsuits and attorneys and risk-management people, and all the worker's comp injuries and PTSD claims, etc. etc. . . . virtually all companies now have policies that their workers are not allowed to place themselves in danger and have to report these things. Companies routinely prohibit employees from even entering a premise with a "loose" dog. If the employee violates these guidelines, and then gets hurt, they potentially face discipline and reduced compensation. The policies are well-intentioned but get amplified by extreme risk aversion.
I'm a dog guy. Have two now. Have had dogs my whole life except for a couple years when I lived in a dorm. And I've had some of the recognized "vicious" breeds too. But your initial post set the stage for this drama. Any dog that's "scary" can cause this kind of reaction. And anyone that has a dog that will bite people is sitting on a time-bomb and asking for trouble.