This is 100% the case in Sweden. Since Uber is a ride service/taxi they are just like any other taxi company, of which there are hundreds (Taxi has one simple definition and it's to offer rides to the public for money). Since there are no artifical caps on number of taxis such as medallions, all that's required to run a taxi is to have a special drivers' license and a certified vehicle.
So all Uber drivers are taxi drivers and all Uber vehicles are taxi vehicles. Simple.
If Uber tried to somehow do taxi services without their drivers having taxi drivers licenses or their cars being registred taxi cars, they'd be laughed at.
Everything is really really simple once there is no taxi monopoly or medallion system.
For Finland it is same. But it seems removing controls of licenses and pricing lead to worse service availability and higher prices... Who would have thought that operating taxi in country like Finland is pretty expensive...
Usually they have a taxi sign on top of the car, and always have blue license plates (which you can only get if you are a taxi).
So, I think that the workaround must have been that they actually employ licensed taxi drivers. This is, however, only speculation.