This keeps getting claimed. No, Sweden is a sovereign nation and its extradition treaties are bilateral - that means they interpret them as they wish.
If they think the demands for extradition are not fulfilled, they can say so, and that's the final word. There's nothing the US or UK can do but complain, there's no court they can apply to to overrule such a decision (because of course, the UK or US governments would certainly not allow themselves to be overruled by any independent court in a matter like this).
The national courts can overrule the government and say that an extradition is illegal, even if government wants to extradite. But the converse is not true: if the court thinks that an extradition would be permissible, the government can still stop it. They can even promise this beforehand, preempting the need for a court ruling. See sovereignty, again.
At worst this would be "impolite". The government of course loathes to do something like this, because then they have to answer for all the cases they did not intervene in with the courts and the civic service's many rulings. They would like to wash their hands of unpopular decisions. But they do in fact intervene quite a lot.
That the government claims "we must not meddle with the judiciary" as some holy principle is darkly ironic in this case. Because if you don't think it was political that Marianne Ny revived the case after it had been firmly dismissed by the previous prosecutor, how naive are you?