Sweden operates on a different legal system then the US and England does which often confuses Slashdot posters.
When a government entity wants to do something it has two options, either it makes a department for it such as the police or firemen. Alternatively it can create a corporation with a CEO where the board of directors are the elected politicians.
A corporation is legally no different from any other corporation, the only difference is that the owner is the county or the state. A number of major Swedish corporations such as Vattenfall are owned by the state.
Furthermore a Swedish county (Komun) is an administrative body, not a legislative one. While they can create ordnances they have no legislative power to grant anyone police powers, that is something that has to be done by the parliament.
While we a few years ago introduced the system where public events have to pay for the police protection, that is not a system where the public event gets to hire the police, that is a system where the police arbitrarily decides how much protection the event needs and then sends them the bill. Their options are to not hold the event or pay the bill, they do not get to choose their level of protection.
The Swedish police does not ever guard common stores unless they are actively investigating crime (For instance lately they've been standing around goldsmiths as gold robberies have been on the rise for years), if a store wants active protection it has to pay guards which do not have much more legal authority then a common citizen (Largely they're legally allowed to physically evict you).
People commissioned by the Swedish government can't be fired (To protect them from political pressure) however they can be replaced. That is they get to continue with their current salary for the duration of their term while someone else gets to do their job. The cabinet only appoints the top level directors who are then supposed to be able to handle everything else. I'm not sure about the exact hierarchy of the police but I believe there's at-least 4-5 levels between the cabinet and Stockholm City Police not counting the various oversight boards.
The cabinet also has a very limited ability to control the priorities of their departments, this is the relevant bit of law
"No public authority, including the Riksdag and the decision-making bodies of local authorities, may determine how an administrative authority shall decide in a particular case relating to the exercise of public authority vis-Ã-vis a private subject or a local authority, or relating to the application of law."
Essentially while the Cabinet controls the budget of the department, makes the commisions as well as perform various executive decisions. They can't legally tell the department how to apply the law.
For example when it comes to Filesharing it is illegal but it's on near zero priority for the police because it's a non-jailable offence (Like not paying the ticket in the metro). If the justice minister told the police to prioritise that she would go to jail for constitutional crimes, her only option is to either get the Riksdag to change the law so it's a jailable offense or require the police to focus on non-jailable offences in general.