Messy situation and I feel really sorry for those people affected. I'd be gutted.
My guess is that the police feel they have no option on health and safety grounds.
I could imagine a way of printing duplicates and getting ticket holders on their seats before the rest of the ground was opened - but what would happen outside?
1. If 1,600 out of 24,000 people are affected that means over 93% know they are OK. They have every incentive to have a few drinks and turn up at the last minute.
2. The people who are worried they might be refused entry are not going to turn up well in advance so that they can be weeded out. They will turn up at the time of maximum confusion (least checking) just before kick off.
3. Even if people could be effectively challenged outside the stadium they are not going to just shrug their shoulders and trudge back home. They will argue for all it's worth.
4. Despite the bravado about refusing entry, I do not see how you can prevent most of the 1,600 from getting into the stadium. If they have any sense, they will then take a place somewhere else.
5. Even if they can be identified inside, how many police and stewards would it take to evict 1,600 people just before kick off? There is every chance that bona fide ticket holders would feel sorry for fellow fans who'd been ripped off and might obstruct the evictions.
6. At the very least, there would be a large delay in kick off time. Given that this game is transmitted live to a huge number of countries, there would be great reluctance to do this. Many of these countries may not wish to change their TV scheduling and would just cancel, causing a major loss of revenue.
7. The result - up to 1,600 excess people in the stadium, breaching health and safety certificates. If there were any sort of incident the police and stadium authorities would be in deep, deep trouble...
The bottom line is that you'll probably get in with a stolen ticket but there is no way the police can admit this.