That sounds similar, but is significantly different, and can be a major pain when dealing with people or businesses that believe the myth, and try to send important paperwork to a physical address, which may end up in our P.o. box if the USPS person handling it recognizes the name and can match it to a box number.
Putting both the physical and P.o. box addresses into an address block, in that order, works well, but then shippers can balk at finding a box number. (see also “Falsehoods programmers believe about addresses, etc.”)