I think when they say USA is the greatest democracy they re speaking of its size, land size.
It's always been a kind of mix between an oligarchy and democracy, just look at the 2 party voting system, extreme wealth required to candidate and the lobbies expenditures.
That's very close to the antiquity democracy, they just need to remove woman right to vote (next one after abortion).
At least with trump we will have a good laugh once again.
The US voting scheme is far from being the most democratic.