It's proven by the many people that were picked up before they could make their attempt because the VoPo's picked up on that before they could actually do it.
These guys would happily turn in their mothers if that's what it took to rise in the ranks:
https://en.wikipedia.org/wiki/Volkspolizei
A bit of 'big data' (to use a popular buzzword) magic would have turned up the names of the two buyers of fabric from the story linked in mere seconds.
Your experience with passengers exiting planes is probably not comparable unless it is in a country like Israel or North Korea. Keep in mind that it wasn't that the police was looking to stop particular people at the border but that they were simply trying to stop everybody from leaving (which tens of thousands if not hundreds of thousands would have done if given the opportunity)
I've written a bit about what it was like to be in Communist Poland here:
http://jacquesmattheij.com/a-western-kid-living-in-communist...
Joke from the era:
Erich Honecker (https://en.wikipedia.org/wiki/Erich_Honecker) has been abroad for a state visit and returns home. Upon reaching Berlin looking out from the windows of the aircraft he notices that the streets seem very quiet. After landing this is confirmed, they drive around for hours on end without encountering a single soul. Finally, in desperation they drive up to the Berlin wall and search along side it, when they reach a very large gaping hole in the middle. Next to the hole is a wooden post with an envelope stapled to it, addressed to Honecker. He opens it and finds a note inside:
"Honecker, du bist der letzte, mach bitte das Licht aus...".