* - We might partially have borrowed this from China.
Modern liberal democracy comes from the revolutions in the 17th and 18th centuries. Greek poleis were at most an inspiration, like the ancient Olympics for the modern ones.
Unfortunately, there are a lot of people in the US who think American liberal ideals are, in some more-or-less abstract manner, descended from ancient Greece or ancient Rome. Maybe it's our neoclassical state buildings. I'm not sure.
The British deliberately sinofied their civil service starting in the very early 19th century, and the US didn't properly get a civil service system until late in that century, so I'd be pretty surprised if that's not the case (at least, second-hand, by way of observing and imitating Great Britain)
As for the ancients, I'd buy that our connection to either Athens or the Roman Republic is largely superficial and was mostly upper-class ego-stroking affectation, but I definitely think it leans much heavier toward the latter than the former. Our symbols like the fasces and eagle, Washington's famous and surely-self-conscious imitation of Cincinnatus, that kind of thing.
Of course your overall point is correct.