I live in Switzerland, where this is the case. Even the government doesn't get this information. If the government thinks you're cheating on your taxes, they have to use warrants and follow the same procedures as for any other crime.
The only financial records accessible are records of legal debt collection actions ("Betreibungen"). Before offering someone credit, you can find out if other people had to sue them to collect.
Yet, even with so little information - without credit reporting agencies - everything works just fine.
FWIW, due to international pressure (things like FATCA), Swiss law was changed so that banks do report on international customers.