Not true. The post office is a federal building and the parking lot is federal property meaning federal law applies. Regardless of state possessing a weapon on the grounds of a federal building is illegal.
This statement is not entirely true. If the post office is in a strip of business shops and is not distinctly separated from them with physical barriers then you can walk right past the post office on the common sidewalk, park in front of or around it and you would be fine. Same thing if the post office is in a business, such as a grocery or hardware store. As for a post office in a strip with other businesses, cannot enter such a post office when armed since then you would be on post office property. Not sure how it would be handle if the post office was within a private business (the grocery or hardware store example). In that case, you could enter and wander around the business while armed, providing the owner allows this, but what about if you decided you wanted to purchase stamps? Would there be a line of demarcation where you must not cross while armed? Not sure about this one.