You are right, the city believes they have ownership of the data, mainly because they fail to understand that they aren’t showing data in an app, but rather publishing data in an API. In Swedish law, once you have released data from a government, the receiver have the right to do whatever they want with the that data (as long as it isn’t violating any other laws).
The city in this case is responsible to check that the data is safe to share publicly and once they have- the data is not theirs. This is regulated in the constitutional law regulating free speech which goes back to year 1766.
This means that they can’t really apply the same logic as a private company can when publishing data in their api. A private company can still keep license over what can be done with the data they publish. A city can not do that because of these constitutional laws.