Or even walked out dressed like a cop!
(Not super serious about this, but nothing would surprise me. And I have to say, that would be a great stunt. Who looks closely at a cop’s face? Like the delivery guys, people see the uniform.)
That was done in the Dorothy L. Sayers classic mystery novel, Murder Must Advertise.
The key here would be to avoid realtime cameras : any photos after the fact, would be closing the barn door after the horse had escaped. It would depend on whom it was, they were attempting to fool.