There are lot of fakes floating around asia as well. What usually gives the game away is the QR code that a lot of official labs are starting to use. If it doesn't link to anything or there is no QR then they know. Also, even if you edit the name from a printout from someone else's test and try to pass it off as yours they can still check the lab and see it's not yours.Even though Brazil requires a PCR test, they didn't even ask me for mine, nor the stupid health form that the airline harrased me to do before boarding. I think you would have to do a really botched job to make a fake test that wouldn't pass in most South American countries, i can't imagine most aduana agents care unless they can get a nice propina out of it
Of course the reality is if someone wanted to create a more complicated fake they could just clone an official lab's website url and all with just a redirect. Then have a QR code which directs to that cloned (fake) site instead of the actual site.
At the end of the day if you are willing to go through all that trouble it's better just to get the swab.