Funny how with Germany's extensive paperwork bureaucracy where every little detail must be recorded and tracked, the healthcare workers couldn't catch this guy earlier.
It's precisely because of this extensive paper-based bureaucracy such things happen, not despite of it.
German bureaucracy is a complete and utter mess. By and large, it's a self-perpetuating end in itself that doesn't serve any purpose other than keeping itself (and the people and organisations involved in it) alive.
Which is more, due to the Germany aversion towards digitization and digital processes (with a misconceived notion of privacy commonly known as "data protection" in Germany often used as an excuse) the data recorded by those bureaucratic processes basically is stored in a gargantuan pile of paper nobody is able to make sense of.
It took more than a month, including placement in a refugee centre, before the administrative wheel stopped turning and it was realised that he was, in fact, only a tourist visiting Germany.
https://edition.cnn.com/travel/article/chinese-tourist-mista...
https://www.dw.com/en/chinese-tourist-mistaken-for-a-refugee...
and from the experiences I had, the people that ran them, and their sheer abundance, this number is probably a very conservative number, and it doesn't include yet all the ones that operated on the brink of scamminess. There wasn't a need to completely and obviously fake the numbers to funnel a lot of public money into your pockets, often without providing any tangible benefit (no qualified personnel, unreliable tests, inadequate execution).
Way into 2021 many streets in the city I live in had one improvised testing center next to the other, mostly ran by people without any medical qualification, using tutorials from the internet and a process almost designed for corruption, where setting up a test center was a state-funded get-rich-quick scheme for quite a while.
[1] https://www1.wdr.de/nachrichten/landespolitik/betrug-corona-...
And there was required documentation, it was just not checked at the time. Once the situation settled down, the state started clawing back fraudulent claims.
That was by design, to facilitate and speed-up the vaccination process, and in the context, there was nothing wrong with that approach to keep the population safe and the country running.