I'm pretty sure most news outlets would cave with the right pressure, with or without any new laws. On top of that is the fact that the department for foreign affairs is the department where the line between ministry and department is the thinest* - I wouldn't be the least bit surprised if, in such a scenario they'd be asked, especially by the US, to put a stop to something, they'd actually put (unofficial, undocumented) pressure on the entity or person in question.

* As opposed to most democracies ministerial rule is highly frowned upon in Sweden, and as a minister you can't issue official decrees that govern how the department itself interpret laws or conduct its business. Instead you (e.g. the parliament) change laws and society act accordingly.