Rule of law is being followed. A lower court judge ruled that there was a risk that Assange's well-being could not be safeguarded in the American system. A higher court judge reversed that ruling on assurances from the US that his well-being would be guarded. Now they have an opportunity to an appeal to a still-higher UK Court.

What's inconvenient here is that the rule of law is operating in the context that the US and UK are allies and therefore take each other's statements on good faith. The United States assures he will be protected, they are not an enemy nation, and there are extradition treaties between the US and the UK. Unless the UK has some kind of carve-out for countries with bad track records of keeping their word, that might be sufficient to satisfy the rule of law.