They do check, but as long as you are within the limits of the country you've arrived to, you're fine:

http://www.taxfreetravel.com/Duty%20Free%20Arrivals

There is quite a long list at the end of the article about arrival duty free. More and more airports are now combining departure and arrival halls so they don't have to run the shops twice. I know ZRH just finished the conversion, with SIN long existing anyway. I'm seldom buying duty free anyway, but for those who do, this is indeed making things easier.