That's pretty dense, going to take a while to really grasp it. But they said we have low checks and balances and low judicial independence. I don't know how true either of those claims are. Here in the U.S. they're inter-related though.
The US didn't really rank low, but lower than other advanced countries.
Weaknesses I can see in the US judicial system:
-Politicians appoint judges and prosecutors. Many other countries have a professional core of judges and prosecutors selected by public examination that then vote among themselves to promote the best or most experienced to higher courts. Other countries, which in my opinion is the best way, have a mixed system, where professional judges appoint other judges for promotion and politicians can vote to allow or deny it.
-Politicians can give pardons to criminals, including other politicians. Most famously Ford pardoned Nixon. That looked like some banana republic thing you would expect in Latin America.
These comparisons are always somewhat hard to make. For example, US federal prosecutors (U.S. attorneys) have different competencies than in many other countries. In some countries the equivalent prosecutors are tasked in prosecuting members of the government themselves, including the president, so they obviously cannot be chosen or fired by the president.
Regardless of that, it seems a very emotive subject for Americans. I've many some Americans who think their country is the only one in the world that has checks and balances or judicial independence. Or freedom. Or that it was even an American invention, but almost all of these ideas came from Europe (Montesquieu, for example) and although it might have been somewhat true that the US led these areas until the 20th century it just isn't the case anymore.
Although the US has, by far, the most fair and democratic way of large countries (Russia, India, China, Brazil, US*), there are smaller countries which are just more democratic, the rulers more accountable and the system fairer, for example, Switzerland.
*Russia and China are dictatorships. Brazil has an European/Scandinavian style system in theory but it's manned almost entirely by criminals or incompetents who will not apply the rules against themselves. I can't understand India.