I think South Korea and India have handled this virus better than any other country.  These are both densely populated nations that responded differently.  India just locked down the entire country very early on.  South Korea did its mass testing well while tracking down folks who might have been exposed to those infected.  

When comparing other countries we need to consider all these different foot races that start at different times.  Europe was heavily hit earlier and has seen what we hope is the brunt of this thing.  That's why Germany's numbers are really good.  Russia is just starting to get the virus really bad.  We won't be able to decipher who has done the best at controlling this thing until after the virus is decimated.  We'll learn a lot from that data.

As for Trump's comments, very early on it was true that the US and Germany had the best numbers of the major western nations. However, the US hadn't hit the worst stretch yet while Germany had.

The advantage Germany and South Korea have over the US is they don't really have to deal with federal and state clashes of authority.  We have the issues of governors of wanting to do one thing and the federal government is limited on what it can do by the Constitution.  

If Trump were to order everyone in the country to stay inside and authorize the tracking of those infected, that would be a death sentence for his presidency.  What's worse, a few more deaths and our country is back to cowering down to foreign nations and our economy is destroyed?  There's a lot of countries that want Trump out of office so they can start taking advantage of US handouts again.

In the end it's the state governments that have the ability to do what's important for their states.  Some have done well and some have not.  Most of them that haven't done well happen to have democrats as governors.