Going back and re-reading it, it seems that they can come over and arrest you at your home - no other law enforcement agency would be involved ... sort of like an international police force going where ever they want and doing what they want regardless of any countries laws protecting their own citizens ...
Well, if they did that it would piss off a lot of people.
The trouble with these changes as I see it, is primarily that they will now have the status of a Ambassador, where they can't be impeded or their assets seized, should we want to stop them. Embassy staff and other A'holes with this sort of protection have made a mockery of US laws many times.