A parking lot where a postal office resides is not Federal land, it's not part of DC it's still Texas. Your interpretation also doesn't prove that any parking lot with a post office in it falls under the control of the post office. Say someone owns a shop that shares a parking lot with a post office, the post office cannot tell that person that they can not have a firearm in their car because it's completely legal in this state to do so. The rules of the post office don't extend beyond its doors or its fenced in loading area.
Most Post Office parking lots are Federal Property. Sure if the PO rents mini-mall space that might not be true, but most POs I have seen are standalone structures on self-contained property.